Electric Circuits - Basics of Electrical Engineering | GoFig Trainings | Skillshare

Electric Circuits - Basics of Electrical Engineering

GoFig Trainings

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47 Lessons (4h 21m)
    • 1. Introduction

      1:32
    • 2. 101 Chapter objectives

      1:16
    • 3. 102 SI Basic Units

      2:06
    • 4. 103 Derived Units in SI

      3:54
    • 5. 104 Prefixes for Powers of 10

      2:53
    • 6. 105 Difinition of Voltage FET

      2:14
    • 7. 106 Difinition of Current MET

      2:00
    • 8. 107 Ideal Basic Circuit Element MET

      5:27
    • 9. 108 Passive Sign Convention MET

      2:33
    • 10. 109 Power and Energy MET

      1:57
    • 11. 110 The Power Equation MET

      2:05
    • 12. 111 The Algebraic Sign of Power MET

      4:23
    • 13. 112 EXAMPLE Algebraic Sign of Power MET

      3:37
    • 14. 201 Introduction and Objectives MET ResisterSpellings

      2:18
    • 15. 202 Voltage and Current Sources MET

      4:25
    • 16. 203 Independent and Dependent Sources MET

      2:46
    • 17. 204 Circuit Symbols for Dependent Sources MET

      6:48
    • 18. 205 Electric Resistance b

      5:16
    • 19. 206 Ohm's Law b

      4:37
    • 20. 207 Power in a Resistor b

      4:06
    • 21. 208 EXAMPLE of Power Calculations b

      13:48
    • 22. 209 What exactly are Electric Circuits

      1:59
    • 23. 210 What is Circuit Analysis

      1:47
    • 24. 211 What are Branches in a Circuit

      3:00
    • 25. 212 Nodes in a Circuit

      5:02
    • 26. 213 What is a Reference Node (or Datum Node)

      3:51
    • 27. 214 EXAMPLE of a Reference Node

      8:32
    • 28. 215 What are Loops and Meshes

      7:18
    • 29. 216 All about Series and Parallel Connections

      4:33
    • 30. 217 Example of Series and Parallel Connections

      2:55
    • 31. 218 EXAMPLE

      8:06
    • 32. 219 Introduction to Kirchoff's Laws

      0:52
    • 33. 220 Kirchoff's Current Law (KCL)

      1:45
    • 34. 221 EXAMPLE of KCL

      8:14
    • 35. 222 Other forms of KCL

      2:42
    • 36. 223 Kirchoff's Voltage Law (KVL)

      2:52
    • 37. 224 EXAMPLE of KVL

      11:08
    • 38. 225 Other forms of KVL

      5:21
    • 39. 226 EXAMPLE of using Ohm's and Kirchoff's Laws to Solve Circuits

      19:44
    • 40. 227 Circuits Containing Dependent Sources

      10:14
    • 41. 228 EXAMPLE 2 of Circuits Containing Dependent Sources

      12:27
    • 42. 302 Resistors in Series

      10:26
    • 43. 303 Resistors in Parallel

      12:37
    • 44. 304 EXAMPLE of Series and Parallel Resistors

      15:04
    • 45. 305 Voltage Divider Circuit

      7:37
    • 46. 306 Effect of Load and Tolerance in Voltage Dividers

      5:05
    • 47. 307 EXAMPLE of Resistance Tolerances in Voltage Dividers

      7:36
20 students are watching this class

About This Class

Start Understanding and Solving basic Electric Circuits easily and confidently!

If you are looking for a course that will help with your understanding of Electric Circuits and basic Electrical Engineering concepts, this course is for you.

Electric Circuit are the fundamental building blocks of all Electrical and Electronic Systems, and you definitely need a solid understanding of these concepts to advance in anything Electrical in nature. This course is the best way to jump right in and start understanding/solving Electric Circuits confidently, like never before.


This course will cover everything you need to know about Electric Circuits:

  • The SI Units and Electric Quantities

  • Electric Circuits and Circuit Analysis

  • Passive Sign Convention

  • Power And Energy

  • Independent and Dependent Sources

  • Ohm's Law

  • Kirchoff's Current & Voltage Laws

  • Power Calculations

  • Nodes, Branches, Loops and Meshes

  • Series and Parallel Connections

  • Solving Circuits with Dependent Sources

  • Solving Linear Equations for Electric Circuits

  • So much more!


By the end of this course, your confidence in dealing with Electric Circuits will soar. You'll have a thorough understanding of how to solve basic Electric Circuits.

Go ahead and enroll in the course, see you in lesson 1 :)

Transcripts

1. Introduction: you're here because you want to master the D C electric circuits, right? This is the perfect course for you. If you're a complete beginner and want to understand, solved and design electric secrets in this course, you will learn everything you need to understand, solve and design electric circuits. We will start from the basics off S I units and electric quantities to circuit elements and how to use them. Passive sign convention and its use it while soldering circuit problems. Electric energy, power and how to correctly perform power calculations. Independent and dependent sources. Holmes Law, Kickoffs, voltage and current laws. Important terms like branches, Nords loops and measures series and parallel connections. Solving circuits with independent and dependent sources. Solving simultaneous equations to solve seconds and so much more whether you're a student off electrical engineering or a professional looking to refresh your circuits concepts or anyone who wants to learn about circuits and electronics from scratch, I have designed the scores to take you from a complete beginner to a circus master. I saw that you could feel comfortable dealing with electric circuits and roll now and master the electric seconds today 2. 101 Chapter objectives: Hello and welcome to this lesson. Now you're going to see what are our main learning objectives for this section, Or basically, what should he expect to learn by the end off this section? So the first objective is that we should be able to understand the S I units as I stands for System International. So we should be able to understand these units and how these are used in electric and electronic circuits. Our next objective for this section is that we should be able to understand the meaning off the terms vaulted current and how these are related to each other. The third objective is that we should be able to understand and be able to use definitions off power and energy which are very important quantities related to electric circuits. And last but not the least. Our objective is to be able to use the passive sign convention to calculate power off a basic circuit element if we know the voltage and current for that particular element. So these are our mean learning objectives. So let's start by looking at the S I units in the next lesson. 3. 102 SI Basic Units: Hello and welcome to this lesson. Now we're going to talk about the international system off units also abbreviated as the S i units. So as it turns out, modern engineering is a multi disciplinary profession in which teams off multiple engineers work on projects and they can communicate the values off different perimeters only if they are using the same units off measurement the international system off units also abbreviated as s I unit is used by all the major engineering societies and most off the engineers to our revolt. The S I units are based on seven quantities. As shown here, these seven quantities are length, mass time, electric, current temperature amount off substance and luminous intensity. So here in this table, we're summarizing all those seven quantities the basic units for each off those quantities and the symbols used for those basic units. So, as you can see, the basic unit for length is meter for mass. It is kilogram for time. It is second and so on. So these are the basic units and similarly, we can also mention here the symbols used for mentioning these basic units quickly and easily. The symbol for meter is small m. The symbol for kilogram is small. Katie for second is small s for electric current in em peers, it is capitally for temperature. In Calvin's, it is Capital K For more, it is small m or L and for candle are it is C. D. So please nor down here that only do off. These symbols are in capital letters, including the air for em peers and K for Calvin. All other letters for these symbols are in small letters. So these are the seven basic as I units. That's it for this lesson and I will see you in the next lesson. 4. 103 Derived Units in SI: hello and welcome back In the previous lesson, we saw the standard as I units. But there are many nonstandard units we use in our daily lives. For example, re frequently use hours and minutes for time, feed and yard for length bound and house for mass etcetera. So the seven basic essay quantities can be combined to form derived units that we also commonly used for quantities like energy, power force, acceleration, electric charge, etcetera. Which I'm sure you have heard off in basic physics or in daily lives. The derived units we're going to use in the scores are summarized here in this table. So in this column we have the quantities. And in this next column here we have in front, off each quantity. We have the unit for that particular quantity, followed by its symbol in brackets. In the last column, we have the formula for each off those quantities. So let's start with frequency. We know frequency is the number off cycles per second. So here the unit for frequency is hers, and its symbol is Age Z. The formula for hers is second inverse or our second. Similarly, for force, the unit is Newton ended symbol is capital. And so, as we know, F is equal to M A. So force is equal to mass times acceleration where two unit for mass is cagey and for acceleration it is meter per second scare. So when we combined the units for mass and exploration, we get the formula for force, which is cagey time, meter por second scare for energy or work. The unit is Jewell and its symbol is capital CI, and the formula for jewels or energy off work is Newton Times meter for power. That unit is ward with a symbol off capital W and its formula is Jewell per second for electric charge. The unit is Coolum with a symbol off capital C and its formula is em. Bears time second for electric potential. The unit is volt with a symbol off capital V and its formula is Jewell por Coolum for resistance. The unit is home with a symbol off this Greek letter. So the formula for homes are electric. Resistance is world for M Pierre and here we have this quantity guard conduct insp, which we know as the opposite off resistance. So the unit for conducting is Siemens and its symbol is this inverted symbol for resistance and at some places they instead off using this symbol for seamen's. They can also use capital s. So just keep in mind that whenever you see capital s written interns off Seaman's nor panic because that is also used sometimes as the symbol for conduct INTs and formula for conductors is as expected, it is Thean divorce off the formula for resistance. This formula was world or in peer for conducting. It becomes a beer over Walt. Lastly for capacitance, the unit is fired. Its symbol is capital F. The formula for capacitance is Coolum. Poor Volt. So these are the derived unit we will be using in the scores. That's it for this lesson and I will see you in the next lesson. 5. 104 Prefixes for Powers of 10: Hello and welcome back. In many cases, the S I unit is either too small or too large to be written conveniently So we have to use the powers off 10 to express them. Standard prefixes corresponding to the power's off. 10 are summarized here in this table. So on the left side, off the stable Here you will see prefixes with negative powers off 10 and on the right side we have the prefixes with positive powers off 10. So we start with 10 days to the power minus 18 which is called Otto with a symbol off small . And we keep increasing thes barbers all the way to turn it stood bar minus one and on the right side. Here we have 10 then tennis to part 2369 12 and so on. So in the middle here we have the symbols for these prefixes and here you can see that all these symbols are in small letters except for the symbol for maga, which is capital M for gig averages, Capital G and tear averages capital t out off all these prefixes. The most commonly used are the ones with powers off 10 which are divisible by tree. Therefore Senti, Desi, Decca and Hecht. Oh, these are used less than the other prefixes also do keep in mind that the rule of Tom is start. We select that prefix in any situation which places the best number between one and 1000. And let me try to explain that with help off an example. So let's say we were trying to express this quantity tenders to the power minus five seconds using one off these prefixes. So either we could write this as 0.1 2nd or we could write this as 0.1 millisecond or 10 microsecond or even 10,009 a second. So technically, all of the's would be correct. But the best choice off out of all these prefixes would be the one that would lead to a base number, which is between one and 1000. As I just said, So keeping that rule of Tom in mind the best choice would be 10 microsecond, because here you can see that the base numbers between one and 1000 for all the other options based numbers, are either less than one or greater than 1000. So in this way you can choose the best prefix for any situation, so I hope this is clear. And now you know how to use the prefixes for powers off then. So that's it for this lesson, and I will see you in the next list. 6. 105 Difinition of Voltage FET: Hi and welcome to this lesson. The concept off electric charge is the basis for describing all electrical phenomena. So here it's a good time to review some important practice ticks off electric chart. First off, all we should know that charge is bipolar in nature, which means there are both positive charges as well as negative charges. Then all charges exist in multiples off the charge on an electron, which is equal to 1.60 to 2 times 10 raised to the power minus 19. Coolum, which is from the basic physics, then separation off positive and negative charges, leads to something called an electric force, which is generally called voltage and similarly motion. Off these electric charges leads to an electric fluid, which we call current. No. As we know, positive and negative charges attract each other. But whenever positive and negative charges are separated against this force off attraction , some energy is required. Imagine you had two magnets in both your hands. You bring them close and they start attracting each other, so if you don't apply any energy, they would hit each other in order to keep them at a distance or to keep them separated. You have to apply some energy. So in the case, off charges voltage is the energy bore unit charge created by the separation off charges. And hear this Number four, This is the official definition off voltage. This ratio can be expressed in differential form as this V equals two dw over de que we're off course V is voltage in volts. And here we're talking about the S I units or as I derived units, then w is the energy in jewels and Q is charge in columns. So that was all about the definition off worlders. And in the next lesson, we're going to talk about the definition off current. Thank you for watching, and I'll see you in the next lesson. 7. 106 Difinition of Current MET: Hi and welcome to this lesson. Now you're going to talk about the definition off current. So as we saw in the previous lesson, moving charges established a floor off charges. So the rate off flew off Charges is known as the electric current, and we can express this mathematically as I equal su dic You over d d where I e is de current in amperes. Q Is the charge in Coolum and this d is time in seconds. So again orders that here we're talking about the S I units are the derived s I units, we already started The charges are bipolar in nature or basically these are off two types. So this requires that we assigned polarity references to both voltage and current, which we will do in the upcoming lesson. One more important thing is that we always treat current as a continuous variable in start off a discreet variable, at least for the purpose off this course. And the reason is that although we know current is due to the movement off individual electrons which are discreet right here I have shown this in the picture, but you can see that any practically significant current involves electrons flowing in huge numbers. Just think about how small the charge often electron is. It is on the order off terrorist war minus 19 Coolum, as we saw in the previous lesson. So even if we're talking about micro amperes are 1,000,000 piers. We're talking about billions and billions off these electrons so we can think off these electrons and their chars as a smoothly flowing entity. So we will always consider this current as continuous variables instead off discreet variable. So I hope that makes sense. So that was all about current. And in the next lesson, we will start talking about circuit elements, so talk to you soon. 8. 107 Ideal Basic Circuit Element MET: hi and welcome to this lesson. Well, the basic circuit elements form the building blocks for constructing bigger circuits. So in this lesson, we're going to talk about the ideal basic circuit element, which has three characteristics. The first characteristic is it has only two terminals with which it can be connected toe other circuit components. The other cracked a stick is that it is described mathematically in terms off either Walters or current or port, and the last characteristic is it cannot be subdivided or reduced into other elements. Hence, we use the term basic because it cannot be further broken down into simpler elements. This figure is a representation, often ideal basic circuit element. The box right now is black because we're not specifying right now what kind of circuit element this is. The voltage across or between these two terminals is denoted by re as you can see, and the current flowing between terminals is denoted by I. The reference polarity for world it between these two terminals is indicated by positive and negative signs, while the reference direction for current is shown by an arrow placed along the direction off flow off current. Then here we have a table to further explain the reference directions for voltage and current. So let's start with the voltage forced. The vault is draw from Terminal one. Tau Terminal two is going to be positive because look at this Terminal one. It has a positive sign and Terminal two has a negative sign. So if you go from Terminal One Tau terminal toe, you're moving from plus to minus, so that is a voltage drop, so the water drop from 1 to 2 is positive. And on the other hand, if we go in the opposite direction, the voltage drop is going to be negative or there's going to be a positive voltage, right? So we we can say that the voltage rise from terminal to Terminal One is positive because you can see that terminal who has a negative sign. Terminal one has a positive sign, so we go from terminal to Terminal one. There is a voltage tries and hence we say that it's value is positive. Similarly, we can say that the from Terminal one terminal to the voltage rise is negative because you can see that from one toe, so there is actually going to be awarded drop. And as for this last statement, if you go from terminal to terminal One, you can see that we're moving to a higher voltage. So yes, vaulted dropped from terminal to terminal one as negative because actually it is a voltage rice. Likewise, we can further command about the current We're talking about the direction off flew off charges so the positive charges flow from terminal one Tau Terminal two with a positive value. You can see that this I discourage. This is actually deep positive charges. So these charges flow from terminal one towards terminal Do so their floor is positive. On the other hand, the opposite is also true. The negative joys is floor from terminal due to terminal one with a positive value. So it's like, Ah, the first statement the opposite off. The first statement is also true. So here we had positive charges. In the next statement, we had negative charges. The first statement says from floor from one to do this next statement say's from 2 to 1. So both of these are opposite, which are both positive. Then we can also say that positive charges flow from 2 to 1 with a negative value because if you look at 2 to 1 terminal who has negative charges, Terminal one has positive charges. So when current floors, the positive charges are actually froing from 1 to 2, not 2 to 1. So that is why we have placed on negative here. And if you talk about the negative charges flowing from terminal one to Terminal two, you can see that, actually, between terminal one to Terminal two, there were positive charges flowing, so the opposite charges are the negative charges would be flowing in the opposite direction . So this last statement says the negative charges flowing from Terminal one towards Terminal two is negative because actually, these were positive charges. So for negative charges there signs would be negative. And from here you can nor down that deposited charges flow in one direction while the negative charges floor in the opposite direction. I hope all this makes sense and if not, feel free to watch this video again. And if still you have some confusion, you can always drop me a message or post a question in the Q and A section, and I would love to explain it further to you. Thank you for watching. Now it's you in the next lesson 9. 108 Passive Sign Convention MET: hi and welcome back. So here we have the same figure from the previous lesson and here we could have assigned any reference polarity for world ege and any reference direction for current. It's totally arbitrary and upto us. However, the important thing is that once we have chosen a reference polarity and direction, we must stick to that reference whenever dealing with circuit calculations. Because if we don't do that, we can create confusion leading to incorrect results. The most widely used sign convention applied to these references is called Passive Sign Convention. The statement off this passive sign convention goes like this whenever the reference direction for the current in an element is in the direction off the reference voltage drop across the element, as you can see here in this figure where d current is flowing in the direction off voltage drop from terminal. Want to Terminal two? We will be using a positive sign in any expression that relates voltage and current. Otherwise, we will be using a negative sign. So here, Can you guess what kindof expression were mentioning to when we say that the expression relates world is and current Well, we're referencing to the power because remember, power is voltage times current. So, in simple words, this whole statement says that whenever the positive current is flowing in the direction off reference voltage drop, the power in this particular scenario would be having a positive sign. And if this current was flowing in the direction off reference will did rise, then the power would have a negative sign. So that is passive sign convention and in the following lessons and sections off the scores , we will be using this convention a lot, so make sure you understand it well. And to further clarify it, we will be applying and interpreting this in power calculations in the next few lessons also, nor down that we have discussed the passive sign convention before, even going through any kinds off circuit elements because I wanted to convey that this convention and polarity references neither depend on the type off circuit element, nor on how these are connected with other circuit elements. So I hope that is clear. Thank you for watching this lesson, and I will see you in the next lesson. 10. 109 Power and Energy MET: hi and welcome to this lesson. No, we will talk about power and energy. The power and energy calculations are very important in circuit analysis, mainly for two reasons. Firstly, although voltage and current are useful variables for designing and analyzing circuit best systems. But quite often the useful output off these systems is Norn Electric. For example, think often electric sound system where the input is electricity, but the output is sound. Motor can be another example where the output is motion, there can be many such examples, and these kind off outputs can be conveniently expressed in terms off power and energy. Secondly, all practical devices have limits on the amount off power they can handle before getting damaged. Therefore, while designing circuits, just doing voltage and current calculations is mostly insufficient now let's find the relationship between power and energy from basic physics. We know that power is time rate off expanding are absorbing energy. For example, a 10 kilowatt water pump can deliver more leaders off water per second, compared to a five kill award water pump. So the power off the first bomb would be greater than the power off the second pump from basic high school physics. We know that mathematically energy per unit time can be expressed as b equals two D W over D D, where B is the power in farts. W is the energy or work done in jewels and t is time in seconds. We can also write this as one ward equals to one Jewell per second, so that is how power and energy are related to each other. 11. 110 The Power Equation MET: hello and welcome to this lesson. And now you're going to explore the power in question. The power associate ID with the floor off charges can be determined using the definition off voltage and current we saw from the previous lessons. So it goes like this p is equal to D W over DT and that is equal to DW over the Q times de que over DT. So this whole thing can be written as the times I where p is the power in votes. This re is the voltage involved and this I as current in amperes. And if you're wondering, how did we get these relationships? While the first relationship P is equal to DW over Dede, this is simply the relationship between power and energy, which we saw in the lesson just before this lesson. Then dwr de que that is equal toe the voltage. And we saw this relationship in the lesson on the definition off voltage Similarly, dig you over. DT is equal int toe the current and we saw that in the lesson on current, this relation shows the deep Our associated with a basic circuit element is simply a product off the current flowing through the element and the voltage across that element. Therefore, power is a quantity associate ID with a pair off terminals nor jester terminal but appear off terminals. Moreover, it's also very important to know that rather power is being too delivered toe the pair of terminals, in which case the element is going to be called passive, or whether the power is being extracted from the payer off terminals, in which case that element is going to be called active. To explore that, we have to take a closer look at the passive sign convention from the perspective off power , and we will do that in the next lesson. 12. 111 The Algebraic Sign of Power MET: hello and welcome back In the previous lesson, we saw this question B equals to re I. However, if we use the passive sign convention, this question will be correct. Only if the girl flows in the direction off world did drop across the terminals. Otherwise, it must be written as B equals two minus V I. In other words, if the current flows in the direction off voltage rise across the terminals than the relationship changes to be equals two minus we I. Therefore, the algebraic sign of power depends on the flow off current through the voltage rises and drops. And here in these four figures, we summarized the relationship between D polarity of voltage and current and the borrower question. You can see that the voltage can have two different kinds of polarities and similarly current can have two different directions. So in total, we can have four different guesses. So here, if we mentioned all the British polarities and all the different ways in which current can be re entered, then we can have these four cases in the above two cases, we have one polarity for world is and the lower who guesses we have a different polarity for world. Similarly, for these two diagrams on the left, we have one direction for current. And in these two figures on the right, we have a different direction for current. So these are the four different possible scenarios. Conceptually, the first and the fourth case, which are the case in case did. These are quite similar because in these cases you can see that the current is flowing from positive terminal to negative terminal here. Similarly, current is flowing from positive terminal towards the negative terminal here, although these two diagrams are upside down compared to each other. But the direction off current, as far as the polarity of voltage is concerned, is seem so. In both these cases, the current is flowing towards voltage drop. Therefore, the formula for power is B equals two. Plus we I So here we have used a positive sign and here again, we used a positive sign. On the other hand, if you look at the diagrams B and C in both these cases, the current is flowing from negative terminal to the positive terminal and here again it is frank from negative terminal to the positive terminal and Asper This rule. If the current flows towards voltage rise, we have to use a negative sign. So that is why we used vehicles to minus B. I relationship here and again because to minors we are here. So these two cases are same. And then these two cases are seem And in these two cases, as the positive charges in the current flow through a voltage drop, the's charges lose energy. And if they moved to a voltage rise, as is the case in the diagram B and C, those charges will begin. Energy. Based on this discussion, we can write a general rule for determining the algebraic sign off power. And the first rule is if the power is greater than zero r, it has a positive sign, as is the case in Diagram A and D. This means that the power is delivered through the box are actually bothered, delivered through the circuit inside the box. So in diagrams A and D, the circuit inside this box is getting the powered are the power is being delivered. So that circuit, On the other hand, if the power is less than zero r, it has a negative sign as was the case in diagrams B and see where the relationship was because two minus we I The power is extracted from the box or from the circuit inside the box. So in diagram B and C, the power is being extracted from the circuits inside these do boxes. So I hope that makes sense. And let's try to further explain that with the help off an example in the next lesson. So see you then. 13. 112 EXAMPLE Algebraic Sign of Power MET: hello and welcome back In the previous lesson, we started about the algebraic sign of power, and now we're going to look at an example to further illustrate that concept. So we're going to look at two different scenarios. So in scenario one, let's say v Jews disparity for voltage in this direction for current, you can see that the direction off current is in the direction off voltage rise because the current is going from negative terminal to the positive terminal. So as for the previous lesson, the relationship for power is going to have a negative sign so we can ride be equal stoop minus lee I for this polarity reference, we're going to further assume that as per our calculations, we get these two values for current and voltage in this direction, the current turns out to be four impairs, and with this polarity of voltage, the voltage turns out to be minus 10 words. So if we want to calculate the borrower, we're going toe put these two values in this relationship so minus three times I've air minus on DVI is Manus Stan, I is four. So if he multiplied them, we get power equals toe plus 40 words. So it is having a positive sign or the power is greater than zero. So as per our interpretation from the previous lesson, if the power is positive, that we can say that the circuit inside this box is absorbing this much warts. So it is absorbing 40 words. Or we can also say that 40 words is being delivered. Do the surgery inside this box. So that was the first scenario. And now let's look at the second scene. Are you? In this scenario, we juiced the opposite polarity references here. The upper terminal was positive here. The lower terminal is positive. Similarly, we're choosing the opposite direction for current. Now here you can see that again. The direction off current is in the direction off world age rise so we can write the power relationship as B equals two minus read. I We're going to further assume that as a result off our calculations, we get these two values for current and voltage. The current in this direction turns out to be minus four impairs and devoted. When this polarity is chosen, the voltage turns out to be 10 forts. Now, if you want to calculate the power. Then we're going to simply put these two values in this relationship. So minus 10 times minus four, it turns out to be plus 40 warts. Now, looking at the positive sign off power, we can interpret it like this. The circuit inside this box is absorbing 40 words, or 40 wars is being delivered through the circuit inside this box. So from these two scenarios, we can see that even though we chose different polarity references, our reserved for power is the same. And in fact, we can use any reference system from these figures. And as long as we applied correctly, we will get the same result. So I hope that now you know how to apply the algebraic sign of power. And how do you interpret that? So thanks for watching. And I will see you in the next lesson. 14. 201 Introduction and Objectives MET ResisterSpellings: Hello and welcome to the second section off the course where we will talk about the circuit elements. So let's have a brief introduction to what we're going to cover in this section. So we will learn about the five ideal basic second elements, which are the voltage horses. The current sources resistors in doctors and get pastors. And in this section, we will discuss detractors, sticks off voltage horses, current sources and resisters were going to skip the induct er's and capacities part for no . It's because a lot of practical circuit systems contain just the sources and resistors. Another reason is that it's relatively simple to deal with devoted sources, current sources and resistors. Because the mathematical relationship between these three elements are algebraic, that means that we can learn the basic techniques off circuit analysis using just algebraic operations. The induct er's and capacitors will be introduced later in the course as their use requires us to solve integral and differential aggressions. However, the basic circuit analysis techniques we will learn in this section will be useful throughout the course. Rather, we're dealing with the induct er's and capacitors or not. So here are our learning objectives for this section. The first objective is that we need to understand the symbols and behaviors off independent voltage and current sources dependent world age and current sources and resistors. And here by writing I I mean the current sores and by writing we I mean devoted stores. We also need to learn the homes law, the cage of current law in the Kerchers Voltage law, and we should be able to use them to analyze simple circuits. And lastly, we need to learn how to calculate the power for each element in simple circuits and Jack if the bar balances for the whole circuit or not. So there is a brief introduction to this section and our learning objectives, so let's die right in. 15. 202 Voltage and Current Sources MET: all right, welcome back. And now we're going to talk about the voltage and current sources. But before discussing de voltage and current sources, it is important for us to understand what an electric source actually ISS. An electric source is a device that can convert non electric energy, toe electric energy and vice versa. And here are a few examples. Think often electric battery. So a discharging battery, converse, chemical, energy, toe electric energy. Whereas if the same body was being charged than it will convert electric energy in do chemical energy, a dynamo would be another example. So our dynamo is a machine that can worse mechanical energy to electric energy, and vice versa. So if we were operating this machine in the mechanical toe electric more, which means that if we were rotating its shaft than it will create some electric energy, and in that case we will call it a generator. On the other hand, if we were operating this in the electrical to mechanical moored, which means that we were providing it electric energy to rotate, it's charged. In that case, we will call it a generator. So both off these are sources off different kinds. But the thing to remember about the current and voltage sources is that these sources can either deliver or absorb electric power, generally maintaining either a voltage or current where we and I represent voltage and current respectively. And this leads us toe the discussion about the ideal world resources and ideal current sources. So let's look at them one by one. First, the ideal voltage source, an ideal vaulted source maintains off fixed wordage across its terminals, regardless off harm its current flows in those terminals, so it will provide a steady voltage. Even if the current in the element changes, current changes would not affect its world it in any way. Therefore, the current and voltage are completely independent off each other. Hence, it is impossible to specify the current in an ideal voltage source as a function off its voltage. And now let's talk about an ideal current sores. An ideal current source maintains a fixed current through its terminals, regardless off the voltage across those terminals, it provides a study card even if the voltage across its terminals changes. Hence, we cannot express the voltage across its terminals as a function offer its current because these two quantities are completely unrelated to each other. And here, as you can guess, the ideal world. A source and ideal current sores are completely opposite off each other. Here, it provides a fixed world age. Even though the current may change on this side, it provides a fixed current, even though the voltage across the source may change. Moreover, please nor down an important point here that these ideal circuit elements do not exist. Practically. These are just the idealized models off actual voltage and current sources, and here I have underlined the world ideal and actual. So I deal means that whichever source we're talking about, its quantity would stay fixed no matter what. So an ideal voltage source would provide a fixed boulders no matter what. And similarly, an ideal current source would provide a faith current no matter what. Whereas if we talk about the actual sources, that means that it's quantity may have some variations, so an actual voltage source may have some fluctuations involved. It and actual current source may have some fluctuations in its current, depending on what is happening in remaining circuit that is connected to it. So I hope this was useful. And now you know the difference between an ideal voltage source and ideal current source. So thanks for watching. And I'll see you in the next lesson. 16. 203 Independent and Dependent Sources MET: all right, welcome back. The ideal voltage and current sources can be further classified in do independent and dependent sources. So let's look at both of them. As far as the independent sources concerned, it creates a voltage or current in a circuit without relying on the voltages or currents elsewhere in the circuit. So the voltage our current created by it is fixed. The value off this voltage or current supplied is specified by the value off the independent source itself. Okay, so it is not dependent on any other variable apart from the source itself. In contrast, if we talk about the dependent source, it creates a voltage or current whose value depends on the value off a voltage or current elsewhere in the circuit. We cannot specify its value unless we know the value off the voltage or current on weight difference. So there is the basic difference. The value of voltage or current foreign independence were just depends on the source itself , but the value off the voltage or current for the dependence ors is dependent on the voltage or current elsewhere in the circuit. Now let's talk about their circuit symbols. The second symbols for the independent. Voltage sores and Garant sores look like this and here we can, nor down a couple of things. The first thing is that a circle is used to represent an independent voltage source and independent current source, and the voltage source must include the reference polarity and the value off the supply voltage. Similarly, to completely specify an ideal independent current source, you must include its reference direction and the value off the supplied current, as shown in this figure now coming back to the dependent sources. These are sometimes also guard the controlled sources because their control lies in the voltage or current elsewhere in the circuit, the dependent sources are represented by a diamond shape instead off a circle. Moreover, both their dependent voltage source and the dependent current source may be controlled by either a voltage or current elsewhere in the circuit, so a total off four variants are possible as shown in this figure. So the 1st 2 diagrams we present the dependent voltage sources and the last two diagrams represent the dependent current sources. We will look at these symbols in detail in the next lesson 17. 204 Circuit Symbols for Dependent Sources MET: All right. Now we're going to talk about the second symbols for dependent sources in detail. And previously we discussed that the dependent sources could either be vaulted sores, our current source. And moreover, these horses could depend either on a voltage or current. So this leads us to four possible variants off the dependent sources. All off it. We're going to discuss one by one in this lesson. So here is the first variant off the dependent sources. We're going to use the diamond shape for the second symbols off all these dependent sources . And from this symbol, you can tell that this is a voltage source. Now which kind of world it soars? Well, from this equation, you can see that re S is supplied voltage off this whole discourse and that is equal to a Times re X where they could be any random number. And V X is the world age somewhere else in the circuit that this source is dependent on. So from this equation, we can say that this whole discourse is dependent on another voltage. So this is a voltage controlled world, the source. So we can write this for short, as were taste controlled world source. Now, in order to completely specify this dependence wars, we're going to need a couple things. The first thing is, we need to identify which controlling world age is controlling this world. Its source. OK, there is the first thing, and then we need the equation that relates the supply. Walters, With the voltage that this is dependent on and lastly, forward disorders, we will need the polarity, which means which side is positive and recite is negative. And in this particular source, the controlling voltage is re X. That the source is dependent on the equation is given. We ask equals toe a times we X and the polarity off this world. It's horses already shown in this stagger. So that is how we can completely specify this type off dependent for the source. And the last thing is that we need to know what are the dimensions off this number? A. So in this equation, the left hand side has the unit off words on the right side. We also have the unit off worlds. So this a in this particular case must be a dimension less number. So is dimension less is just a multiplying, constant or scaling factor. So these are the requirements to specify. A world is controlled water source and similar requirements exist for completely specifying other kinds off ideal dependent sources. Let's look at the next type off dependent source and here again we can see that this is a forte source. But looking at this equation, we can see that the supply work is this time It is equal toe b times i x, where I X could be the current somewhere else in the circuit. So here this current is controlling the board days off this world, the source. So we can write this for short as the current control voltage sores, current controlled world source. And as far as the requirement School, the controlling current for this world resources i X, The supply voltage is we s the polarity off the world resources already given and in this particular case, that dimensions off be have to be Ah, let's see, on the left side we only have words. So on the right side, we have in piers and in orderto cancel this m beer and get words so as to balance the dimensions of both sides be has to have the dimensions off world or in peer. So if b has this time engine, World war and beer, then when we multiply, be with I eggs than this imp ear and this comparing the denominator cancel and we will be left with the dimension off walls on the right hand side. So that is how that dimensions word balance, then moving on to the third type. In this case, you can see from the symbol that this is actually a current source. Now, from the equation, I ass equals to see times we acts, the controlling variable is avoided. So this current sources being controlled by a voltage so we can call this a vault is controlled current source world. It controlled current source. And as per the requirements, we can say that we access the controlling voltage. The supply current is I s, which is equal to C times. The controlling voted V X. The reference direction for the current is already given here. The only thing left is C. So as far as the dimensions off Sego, we need the dimensions off in peer over walls. Why? Because on the left hand side, we only have the dimension off in peer. So on the right side, we already have This war's here. So in order to cancel this world and get impair on this side as well, we need to have the dimension off See as m peer over words. So this world in the denominator and this world will cancel and we will be left with impair on this side as well. So that is our both sides would have the same units. So keeping that in mind that dimensions for see need to be impair over world. And lastly, this is the 4th 1,000,000 off the dependent sources which is off course again the current source and from the equation, we can see that the controlling variable this time is also a current So the controlling current i x When we multiplied with the variable d, we get the supply grand for this current source. So I access the controlling government. I s is the supplied current the polarity for the current sources given and in this case he has to be dimension less. Why? Because on the left hand side, we have the units off appear on the right side. We already have the units off M Pierre. So d has to be dimension less numbers so that we have the same unit off Mbare onboard sites . So, yes, in this case, D is going to be a dimensional list number. So I hope you enjoyed this lesson and you learned about the circuit symbols for dependent sources. So thank you for watching and let's move on. 18. 205 Electric Resistance b: hello and welcome. In this lesson, we will talk about electric resistance. So first of all, let's talk about the definition. Well elected resistance is the ability off materials toe impede or resist the floor off electric current or what is electric current is the flow off electric charges, whether these are holes or electrons. So the ability of metiers to resist the floor for electric charges is card the resistance and the circuit element, which is used to model this kind off resistive behavior is guard the resistor. So the symbol for resistor is like this. You know, you know, this little is exacting with two terminals and this is the symbol for resistance, and its value is shown is written just besides that. So here we're just writing a general value are but it is going to be some specific value, as we will see soon. Now, if you think about it, what happens when electric charges are flowing through a material? Actually, when these electric charges this could be electrons. These could be holes and let's assume these are flowing towards left direction through this material. So on their way, they are colliding with the atoms off this material and due to those collusions here is produced so apart off elected energy, which is carried by these charge carriers, some off that is lost in the form off this heat or thermal energy. So some electric energy is lost as terminal energy due to dis collusions between charge gators and the atoms off the material. And this is God resistive heating. So for the most part, this resistive heating is an undesirable phenomena. But they're certain devices where this thermal energy is harnessed to perform useful functions. For example, think about electric stores or posters where this internal energy is used to cook food. Similarly, this term in energy can be used to heat water in the water. Heaters are toe Iran plots now. Different materials have different values off resistance Metals like copper and aluminium have small resistance. So these air used in viers to conduct electric current and in fact, their resistance is so small compared to other elements in the circuit that for simplification, purpose read or mortal wires as resisters, we neglect the resistance and assume that the wiring resistance is close to zero r zero. And now let's talk about the unit off electric resistance. Well, the S I unit for resistance is home OK after a German physicist and the symbol for whom is this Greek letter omega Or let me try again. So this is used as the unit for resistance. Now, when talking about resistance, there's another quantity you should be familiar with and that is guard conduct INTs. So conductors is the reciprocal or inverse off resistance. The symbol for conduct INTs is G, while the symbol for electric resistance is capital are. Let me write it down here. So capital are the North Resistance and Capital G D Norse conduct INTs and the unit for conducting its is Seaman's, which is abbreviated as capital s or another unit for conductors, which is used in some textbooks as move Okay, which is home written backwards. And the symbol for more is inverted America. So if we relate resistance with conduct INTs, then we can write Resistance equals toe one over G homes were g is conducting a service. We said they're conductors is the reciprocal off resistance. So that is exactly written here. Similarly, we can ride, uh, conductors equals to one over r and the unit for conduct INTs is Siemens. Now let's say we have a resistor with resistance off then so R equals 2 10 home and for the same resistance. If we write its conduct, INTs then G would be one over then Siemens. So that would be 10.1. Siemens are 0.1 more or we can also write its symbol inverted omega. So these are the basics off electric resistance and conduct INTs and the relationship between them. I hope you found this useful. So in the next few lessons we will explore more about resistance is so Thanks for watching and see you in the next lesson. 19. 206 Ohm's Law b: Hi and welcome back in this lesson, we will talk about one of the most fundamental laws off basic electricity and that is God Holmes Law and tour. This course we will keep refering back to this law again and again. So make sure you understand this law very well. So whenever we have a resistor and we applies a voltage across esto, it's terminals. A current flows through this resistor, so we need a way toe. Relate these three quantities current voltage and resistance and homes. Lord does exactly that for us, but there are two ways to relate these quantities. You know, basically depending on two cases, the first case is when the current is flowing in the direction off voltage drop. So if you see this is the negative terminal, which means it is at the lower voltage and this is the positive terminal villages at ah, higher voltage. So the difference is this V But when current is flowing downwards, it is flowing from positive terminal toe, the negative terminal, which means it is flowing in the direction off voltage drop. So this is one scenario and the other scenario is when the current is flowing from lower wattage terminal to the higher voltage terminal, which is in deduction off wordage rice. So for both these cases, the question would be different. For the first case, the equation would be V equals two I times are while for this case where the current is flowing in the direction off voltage rice, the you know this aggression would be we equals two minus. I are We're off course V is for voltage involved This small I is for current in em peers. And this capital r is for the resistance in homes. And if you're wondering why we have this negative sign on this case and we have a positive sign in this case, well, that is because off the passive sign convention. So these signs are a direct consequence off passive sign convention. And if you don't know what that is, we explained this passage sign convention in the first section. So please refer back to that if you don't understand what that means. So according to passive sign convention, if the current is flowing in their direction of voltage, drop through resistor. We have vehicles toe ir, and otherwise it is going to be V equals two minus. I are so dis aggression v equals Do I r is guard the homes law and this form is most common equals toe ir with a plus sign because in resistance, as we will see further on in the future lessons, the current or the conventional current always flows in the direction off voltage drop. So this is the equation that is guard the arms law. Now this is simply an algebraic relationship between voltage current and resistance. So we can many plate this algebraic relationship to write it in three different forms. So this is the first form which is exactly like this. So basically, here we have work in return in terms off current and resistance. Here we have current return in terms off voltage and resistance. And here we have resistance written in terms off voltage and current. And depending on the situations, one off these forms might be more useful than the others. As we will see while solving examples off circuit analysis. Now, since owns law is based on resistance, one important point we need to keep in mind is that we will deal with ideal resistors in this course, which means that the resistance off elements will remain constant and it will not very with time. So we will assume that all resisters are ideal and the resistance will stay corn stern. It will nor change with time while in reality it may very due to many factors and the most considerable factor is temperature. But in this scores for simplification purposes, we will assume that it does not very with time. So there is all about arms law. Thanks for watching, and I will see you in the next lesson. 20. 207 Power in a Resistor b: In this lesson, we will learn how to calculate power absorbed by a resistor. And here I used the word absorb because we know that resistors are always going toe absorb or dissipate power resistors will never generate power. Having said that, how do we actually calculate the power absorbed by a resistor? Well, imagine we have this resistor r and we applied this voltage we across its terminals Now, as a result, off this world, it some current is going toe floor in the direction off voltage, Drop through this resistor. Now, with all this in mind, there are multiple ways to find power. And the first way is we can simply multiply the voltage across the resistor and the reserving current through the resistor. So the first way is toe multiply this voltage times this current and that will give us the power absorbed by a resistor. No, Sometimes one off these values is missing. It is not given to us directly. So in that case, we can use one off the two other forms off this equation and ah, to write down those two forms. Let's have a look at this home's law which we saw in the previous lessons. So this was the primary form off homes, law vehicles, toe I are. But since this was an algebraic equation, we could manipulated in and write it in different ways. We could write it as I was to be over our or we could also write it as R equals to be over I. Now let's say that in this equation, instead, off writing re, let's replace this we with its equal and from homes law. So vehicles toe ir su instead of this We I right, I are in this I as it iss so these eyes get multiplied with each other and we get I scared are so this is the second form off this power question, and there is yet another form off this same question. And for that instead off replacing re with its equaling from owns law. That's right. We as a days and instead off I let's replace it with its equal in from owns law I, as Barone's law is, he could do we over our So let's ride we over our now These two wees get multiplied with each other so we get re scare over are so this is the first power equation for a resistor. This is the second form off the same equation, and this is the third form off that question. And these three questions provide different ways to calculate power absorbed by a resistor . And each of these give us the same answer. Now, depending on what information is provided directly in a circuit one off, these reforms may be more convenient than the other two forms. For example, if both voltage and current work directly given to you, then you could directly blood in those values and find power. Using this formula, However, let's say if the current was not directly given to you, either you could use the owns Lord to find current and then put it in this equation or a more convenient way would be to simply skip current and use this form of the power equation where current is not even there leg ways. If the resistor value, of course, was given to you and the current was given, but you didn't know the voltage that in that case this form would be more convenient. So that is how you can calculate Bauer absorbed by a resistor in different ways. Thank you for watching, and I will see you in the next lesson. 21. 208 EXAMPLE of Power Calculations b: hi and welcome. In this example, we will do power calculations for different resistors. So the question is in each off the circuits below find the unknown value for voltage or current. So here you can see the unknown is we won with polarity given similarly here we have unknown I do with the direction off the current given and here we need to find this re three in this polarity And here we need to find I for in this direction and the second part is determined The power to see dissipated in each of these four resistors. So here we have the resistor eight home Here we have resistor and its value is represented in terms off conductors So do keep that in mind. Year we have this third resistor with $20 value and here we have fourth resistor with 25 homes value So let's start with the solution So let's say and off course here we're going toe heavily Use the arms loss who let me write it down here re equals to buy our let's also writers other forms I equals to be over our and r equals to re over I one important step you need to do before solving any circuits. Problem is toe assign one off thes conductors as ground okay, because you know, voltage is the difference between the potential off two terminals. So if we say one terminal is artsy rewards, then the calculations become much simpler. So let's assign the lower point as zero wars and that is represented by this symbol, which is God ground. Now we have said this is zero wars, all the world to desert. Other point would be weird reference to this wordage. Let's come to the first problem here. This current source is forcing one impaired current in distraction. So not think about this. This is a closed part and there is only one part for the current to flow. So this one impair is flowing upwards and from here it will come to the right side and from here through the resistor, it will be flowing downwards. Okay, So for a moment, let's forget about these unknowns and their directions in terms of current and their polarities in terms of four pages. Now, this one ampere is would be flowing downwards through this resistor. So the current through this resistor of would be one and beer flowing downwards. And also we know that for resisters, the current always flows towards the direction off voltage drops. So if this is the wordage, polarity and resistor, the current would be always flowing. The conventional current would always flow towards the directional voltage drop. Now we know the direction off current flu so accordingly, we can say that this has to be positive terminal for this resistor and this has to be the negative terminal. Ah, as birth this rule. Now we know the value for resistance and we know the value for its current. So can we use arms Lord to find his Walters? Well, yes, We can simply put the valley for current and resistors and resistance into this equation. So, Walter, physical do I are so wolf did for this resistor would be I, which is one in peer times are, which is eight homes so worded would be it works in this polarity. Now we can compare the polarity we found out and the polarity asked in the question. So here the positive terminal is upwards and here we have the same positive terminal so we can say that we want equals to eight board No for the second case, since this is your awards and this voltage source is enforcing a difference off 50 words between the terminals off this world resource So which means that the positive terminal off this for the source is that 50 words higher than the negative terminal. And since the negative terminal is at zero wars, this positive terminal is going to be exactly 50 boards. And since this is the same conductor, this is also going to be 50 words all until this resistor Now this is zero wars. This is 50 words. So we know that this is the positive terminal across resistor. This is the negative terminal across resistor. So the voltage across this resistor is 50 force. We need to find the guard so current using this formula, I equals two. We over our I equals do re over our But here we are given this conduct INTs So instead off one over our weaken right we G, which is all these times conduct mints So world age is 50 volts 50 wards Times conduct Mintz is point who Seaman's and when we multiply that 50 times point toe is 10 and since we're finding current, it is goingto be Then in peer using this rule, we know that the current would be flowing in the direction off voltage drop across the resistor and since the direction of what a drop is downwards So this current is flowing downwards and now we can compare the direction off unknown current and the current we just found. Since these are in the same direction so we can write that I do is equal to this currently just 10 amperes. So I do equals 2 10 amperes. Moving onto the third question we have This is zero wards off course Now one ampere is flowing downwards. Now this is a closed part for the circuit and there is only one part for the current to flow. So this one ampere is flowing. It will come in this direction and then through the resistor it will go upwards, OK, and then it will come here and back to the same terminal. Okay, so in this way it is flowing in the nd clockwise direction. And since we know the direction off conventional current flow through the resistor, we can say that the lower terminal has to be positive. The upper terminal has to be negative because the current would always fruit Who resistor in the direction off voltage drop Now what is this voltage? This voltage equals two The current times resistor not What is this current? Well, this one ampere it is the same government which is flowing through this resistor. So one and bear times resistance which is 20 homes. So Grandi forms and this world age is equal to 20 times one which is 20 wort now. Since the polarity off the voters we found out is operated toe the polarity off the unknown world dead. We can say that V three is negatively equals to negative 20 words. And now the last question here This is the water source. So if this is zero words and it is connected to the negative terminal on the positive terminal has to be art. 50 words 50 walls. So this is also going to be 50 wards. Since this is zero wars, this is higher than that by 50 words. So this terminal is positive. This is negative. And also we know that through the resistor the current would always flew in the direction off voltage drop so the conventional current would be flowing downwards. And so far we are totally neglecting this direction off current being asked in the question . So what is this current I well, I equals to re over our now V is 50 words across the resistor. So 50 words divided by what is the resistance? It is 25 rooms. So this I equals to 50 or 25. It is to m Pierre flowing downwards. But the question is, what is the I four froing upwards? So I for equals two minus I which is equal to minus toe, impair because the directions off these two currents are opposite. So we compensate that by putting a negative sign here. So let me underline all these answers the unknown for this question as a reward for this. It is then in piers here This is minus 20 wards and here we have minus toe in Pierce. Now let's come to Bard. Be so here. We need to find the power dissipated in each resistor. So, for a moment, let's forget about this home's law. And let's look at the three formulas for power. So we know that power equals to be I and it is also equal toe I scare are and it is also equal to the scare or are remember three different three different forms off the power equation for resistor. We can use any off these equations to calculate bar for these resistors, and all of them would yield the exact same answer. And after a soldering part A. We have all the unknowns related toe resistors for all the resisters. We know their values, their currents and their voltages so we can pick any off these forms. So let's figure these are one by one. For this resistor, B equals toe. Let's start with the simplest one. Because to me I now, since we know that the resistor is always going toe disappeared power and as per passive sign convention that dissipated power is positive. So we don't need to worry about the science off the world days rt directions off current here We know that the resistor has a positive power because the power is always going to be dissipated in the resistor so we can simply multiply. This world is with current the world ages it work times one in peer one in peer. So power is going to be eight times one, Which is it? Work for the second case. We know the voltage is 50 words across this resistor and we know it's current, so we can use this formula. So world is is 50 and current is and so it is 500. But let's also show you that the different forms will yield the same months or so. Let's write this as I scare are as well. So I scare is dance care which is 100 times are, which is, um you know, this is conductors point to Siemens so the resistance value equal in tow. That would be five rooms. So if I write five and multiply, we still get the same result 500 ward 500 foot. No, for the third case, let's use we scare over our we're old age is minus 20 boards so minus trendy scared over 20 owns. So 20 and 20 scare cancer. So power is going to be 20 board And for the last scenario, the voltage across the resistance is 50 ward, so power is equal to 50 world times to impair, so power isn't going to be 50 times to which is 100. What? So let me underline the reserves for our part B here we have power dissipated as it works here. The power is 500 wars. Here it is 20 words. And for the last case, we have power dissipated equals 200 watts. So in this way we can find the unknown values for World agent guard for simple resistive circuits. And similarly, we confined. The power dissipated in resistors, using different baller relationships. So I hope that was useful. Thank you for watching. And I will see you in the next lesson. 22. 209 What exactly are Electric Circuits: hi and welcome know that we're diving deeper into electric circuits. I think it's a good idea to look at the formal definition off what an electric circuit is. So an electric circuit is a collection off circuit elements connected to gather to achieve a specific goal. For example, a battery connected to an led or a light bulb. Now here the circuit elements are the battery and the led. The wires are used to connect them, and the goal is to convert energy from battery to produce light. Also north that we have represented this circuit in the form off her diagram using circuit symbols to represent this battery and the allergy. And these lines represent the connecting wires, and sometimes we put doors on these connecting wires to represent the connections between the elements. The function off these wires is to allow circuit elements to share currents and voltages and thus interact with each other to achieve a specific goal. These wires to connect circuit elements are made off good electric conductors like copper. Ideally, these wires offer zero resistance to flow off current, which also implies that all the points off a wire are at the same potential and also that all currents entering one end off a wire exit at the other end. So which our current is entering from the battery toe this end off the wire. All of that current would be exiting from this and off the wire into the allergy. Now, although the resistance off these wires is not exactly zero, but at this stage we will assume it to be negligible. And in this course we will treat all connecting wires to be ideal with zero resistance. 23. 210 What is Circuit Analysis: Welcome back. A major portion off discourse is about circuit analysis. So here it is a good opportunity to also look at the definition off circuit analysis off what it really means. So circuit analysis is the process off finding the specific voltages and currents in a given circuit, a procedure sometimes also referred to as solving. The second circuit analysis is based on two sets off laws. The 1st 1 is the element laws. These laws relate the terminal voltages and currents in individual elements, irrespective off how they're connected together to form a circuit. For example, homes Law is the element law for resisters as it defines the relationship between voltage and current off resistor, irrespective off how resistor is connected in a circuit and as we introduce new elements in the rest off the course there, element laws will be discussed then, and the second kind off laws are called the connection laws. These are also guard deserted laws are Kickoffs, laws or kerchief or kick off her. You wanna pronounce it. So these laws related the voltages and girls shared at the interconnections, regardless off the type off circuit elements forming the circuit and before we introduced the connection laws or trick of flaws. There are few extremely important concerts you need to learn. So in the next few lessons, let's go through the concepts off branches Nords loops and measures in serious and barrel connections before formally introducing the gurgles loss. So I'll see you in the next lesson. 24. 211 What are Branches in a Circuit: Welcome back In this lesson, we will talk about branches so each element in a circuit forms a branch. For example, if we have this circuit where we have six elements x one through X six, where X could be a resistor X could be awarded source current sores and so on and so forth . So since this network has six element hence, we have six branches labeled as X one through X six. Now East Branch has a current flowing through it. Guard the branch current and a voltage across it called the branch Voltage. Now here I underline the word true for current. Why? Because you know current flows to a brand. So whenever we talk about current in a brand, we will use the word true similarly for vaulted we know that voltages the difference off potential between two points. So the ends the turns off a branch, the voters. The potential difference between those two wires is guard the world egx. So for a branch worldwide, you would always be across the branch from one point to the other. So that is why we always use the word true for current and the word across for voltage. Now it is very important toe always label the important voltages and currents in the circuit, usually for every element. We use its label as the subscript for writing its world ege and current. For example, here we have the first element labeled X one. So the current through it, let's say it is going upwards. So the level off the current would be i sub x one were where this means that this the current for the Element X one. Similarly, for its vaulted, we have to first mention the polarity and then the world days with the subscript, which is the label off that element. Also note that since current and voltage, both are oriented quantities, which means the voltage always has a polarity and current always has a direction. So if we just right i sub x one and v. Sub x one, without mentioning their direction or polarity, respectively, it is going to be meaningless, and we must always label the direction off current with its label, just like we did here. And similarly, while mentioning voltage, we must always mention its polarity while writing its level. Similarly, we can mention the voltages and currents for all the other branches. But I hope you get the idea. So that is what branches are in the context off electric secrets. Thank you for watching, and I will see you in the next lesson. 25. 212 Nodes in a Circuit: Welcome back. Now let's talk about North. So when the leads off, two or more elements join together their form a note. For example. Here we have gained the same circuit where we had six elements, so you can see this circuit has a total off four north. The first North is where X one and X two are meeting. So let's call it nor a the second Nord is where x two x four Next three are meeting. So let's call it Norby than X four, x five and x six are meeting at this. Nor, let's call it Lord See and the lowest Nord is where x four X fire, Extra A and X one are connecting. So let's call this Nord deep now, if only to Leeds create a Nord that Nordea's guard a simple node. So out off all these four north, you can see that only this first Nord is a simple Nord because it is only connecting two elements X one and x two. This is not a simple Nord because three elements are connecting here again. Three elements are connecting and here we have four elements connecting so it is not a simple nor either. And if the number off leads is greater than to the connections off elements are shown with dots. For example, here we have three elements connecting so so normally we would put a dot here Here again, this is where three elements are connecting. So let's put a dog here here as well. And here now there are a few more important points about north that you need to keep in mind. And the 1st 1 is all points in a Nord are at the same potential and that is guard the north potential. For example, if we know that there is a war, did we ate at this point than all other points on this? Nor would have the same voltage we A if we know that for example, this work is five words than all other points on this nor would have exactly the same voltage. Five words also all points connected together. Two uninterrupted wires form the same note. For example. You know all these points. All these collection off point. These are bars off the same north. This is a separate Nord No, B and C are two separate north. Why? Because these are not connected through uninterrupted wild. There is an interruption here in the form off X four. So that separates Norby and Nord. See if this was just a connecting wire. There was no element here than this whole area would be part off the same Nord. But under current situation, it is not more or a single, nor may have more than one dots, for example. Look at the bottom here we have one door and here we have another daughter. But you can see this is part off the same north because there is no element in between these two doors. These are connected through continuous wires and another important point is that the same circuit may be drawn in multiple ways as long as the elements in the circuits are same and their connections don't change. And just to clarify what this means, let me draw this same exact surgery in a slightly different fashion. For example, let's droid like this. So pardon my bad drawing. So this is element one. This is element toe cree for for you six. Of course, this is not the best drawing, but I think you can understand what this means and for simplicity. I'm not writing these excess. I'm just writing their sub scripts. So here you can see X one and X two are connected through this simple Nord so their connections don't change and similarly, the elements are still the same. Then x three is here in this position and I have drawn x four expire next six in a different fashion x four I have drawn it vertically and below that x five and x six are connected like this so you can see that their connections have nor changed at all. So although there diagrams are quite different but the working off these circuits are exactly the same because we have used the same elements and their interconnections are exactly the same. So the main point here toe show you is that we can draw circuits same circuit in multiple ways without changing their working. I hope this is clear and that was all about north. So see you in the next lesson with another definition 26. 213 What is a Reference Node (or Datum Node): Now let's talk about a special type of Nord card deed reference load, since only the potential differences or voltages have practical meaning. It is convenient to reference all nor potentials in a circuit to the potential off a single common Nord, which is called the Reference North, or sometimes we also refer to it as the data m'lord. This north is identified by the symbol this like the earth symbol you might be familiar with and its potential is zero words. Spend referenced toe the datum, nor nor potentials are simply guard, nor voltages, usually a Nord at the bottom off. The diagram is chosen as the data m'lord. But to simplify second analysis, de Nord with the largest number off connections may be chosen as the data m'lord. For example, here we have three elements in this diagram. There are three north and the bottom lord is taken as the data ignored. There are two other north and let's call them nor a and nor be no if I ride this voltage across X one as V a and this voltage across extra as we be sorry, This this should be capital A. As we're referencing toe this note. So both these we and we be these air nor voltages as they both reference that data M'lord. This means that both of these voltages are positive at the top and negative at the terminal which is the ground terminal or the Tatham terminal. Now, if you want to write potential off nor every dis specter Norby, we will, right? We A b which means that the first confident is taken as positive terminal in the second component is taken as that negative terminal. So if we expand this, this would mean we a minus. We be on the other hand, if we write it in the worse order like if we ride, we be a This means that be this time is the positive terminal minus the V A which is the negative terminal. So in this case, this we A and we be both of these are nor voltages because with these waters is we're referencing the data mode while we a b or vb a both off. These are brand voltages because in both, these voltages were not referencing the data of note. Now, one major benefit off using the debt ignored is that all northern understood to be referencing the data ignored. So we don't even need toe mentioned. The polarity marks on the diagram, making it much simpler. For example, here we have the same diagram. And since we're using the debt in North, it is understood that all the Nords there voltages are with reference to the data. Nor so for this, nor a even if I write this world ages this worded as we a and for this more would be Even if I ride this as we be, it is understood that this is deposited Terminal four we be and the negative terminal is ground similarly for V A. This is the positive terminal, and the negative terminal for that is the data nor or ground. So in this way, our diagrams can be much more precise because we don't have to mention the voltage polarities everywhere. That makes up for a much more concise diagrams. 27. 214 EXAMPLE of a Reference Node: Hello and welcome back knowledge to an example about the reference node, which will further clarify any confusions you might have about this concept. So what we're given is this circuit, which is composed of five elements, x one x two, x three x four and x five So these air connected in this way and were asked to mention all nor voltages if the data nor is first if we take Nord de as the Datum Nord. And in the second case, if North Sea is taken as the debt ignored. So Nords are also mentioned in the question. So if you look carefully, there are five elements enhanced. There are five branches off this circuit. We have four North A, B, C and D out of which, nor a and see these are simple North because they are only connecting two elements while nor D and B These are not simple notes. And also what is given to us is all the brands voltages Remember thes air branch voltages because these are not referencing toe any data? Um Nord. So we're asked to find north voltages at the three north while using the fourth Nord as the data M'lord. So to solve this question here, I have created two copies off the same exact circuit. And in this case, in the first case, we're going to dig Nord de as the Datum north and here we're going to take North Sea as the debt ignored. And then we will find all the Nord voltages. So all this writing in red, this is what came with the question and now I'm going to write the solution with the blue marker. So first of all, in this first case, let's choose White are Nord de as the debt ignored and I'm going to draw this data Nord symbol. And of course, the Statham north is going to have a world age off zero. No, before that let's look at the concept about voltages. So if we have this, let's say this five world voltage source. What this means is that the positive terminal has a five world potential higher than the potential rt negative terminal. Or this also means that the negative terminal is at a five board potential lower than that at the positive terminal. So using this concept, this is the zero World. What is the voltage at North Sea. For that, we have to look at this X five element and its polarity. So it's This terminal is two words higher than the negative terminal, while negative terminal is connected to zero, while Duval's higher than that is going to be Duval's. So North Sea is going to have a potential off do world. Now let's look at the world age off B. For that, we have to reference to x three so it's negative. Terminal is connected to ground, which is zero. So it's positive. Terminal has to be five words higher than its negative terminal, which is zero. So five words higher than zero is going to be five boards, so we be is going to be five gold. And lastly, we have to find the north voltage. Are we A. And what is that? It is by looking at X one, we can see that it's negative. Terminal is connected to ground or zero, and it's positive. Terminal has to be one world higher than its negative terminal. So one world higher than zero is going to be one word. So that is how we have found our all the North voltages for this circuit and weaken further . Verify our reserves by looking at X two so X to its voltage and forces that it's positive. Terminal is four words higher than its negative terminal, so you can see the positive terminal, which is Norby. It is five words, which is four words higher than the negative terminal, which is, nor a read a voltage off one word. Similarly, weaken further. Verify we B and V C looking at x four. So it says that it's positive. Terminal is three worlds higher than its negative terminal, which is true because it's positive. Terminal VB is five words, which is three words higher than we see, which is two wars. So in this way I have already found all these reserves and I have further very fired by looking at x two and x four. So that was part one, and knowledge do Part two, where we need to consider North Sea as the data north. First of all, I will draw this ground symbol. I'll connected toe North Sea making this Nordwall did zero, and accordingly, all other north voltages are going to be affected. However, the Broadwater judges are going to be exactly the same as they are because they're not referencing toe the death of note. Now he can solve them one by one. First off, all the Norby is simplest because here, looking at X for it, says that it's positive. Terminal is three worlds higher than the negative terminal. Now negative terminal is connected to zero. It's positive. Terminal, which is three words higher than zero, has to be plus three wars. So we be is three board. Now we d here. You can see that this x five and forces that it's positive terminal is two words higher than the negative terminal or otherwise. You can also say that it's negative. Terminal is two words lesser than its positive terminal. Now, positive terminal is connected to zero. So two worlds lesser than zero is going to be minus two worlds. So in this case, we D has to be minus to work. Similarly, as from the knowledge about North, we know that all these points on a single lord are going to have the same potential. So if this end is minus toward this end, is also going to be minus toe work. So let me write it down here, although there is no need to. Now, let's find out the potential or normal dates at a this X one. It's polarity enforces that it's negative. Terminal is one word lower than the positive terminal or its positive terminal is one world higher than the negative terminal. Now the negative terminal is minus two volts going from this point, nor D to north a from minus two words. I have to further add one world toe reach point A so minus two word plus one board is minus one word, which means wordage at point is going to be minus one fort. So these are our solutions, and we can further verify them by looking at the polarities across x two and x three. First of all, the polarity across X to enforce is that it's positive. Terminal has to be four words higher than the negative terminal. And if you look at the difference between we A and we be, that is also exactly four volts. So we be is four words higher than we A, which is exactly what this is enforcing. So our re and re be are correct, similarly x three and forces that the difference between we be and Reidy is going to be five wars. And if you look at B B, which is three words and VD, which is minus toward the difference between them is exactly five words. So that is how we can tell that our solutions are correct. So I hope this further clarifies the concept off reference. Nord, Thank you for watching and see you in the next lesson. 28. 215 What are Loops and Meshes: in this lesson, we will look at the definition off loops and measures with the help off this diagram. So first of all, a loop is a closed part in a circuit so that no Nord is crossed more than once. So there is the definition off loop, and also a mash is a loop that contains no other loop inside that No, what do these statements actually mean? Well, let's look at this diagram to clarify that first of all, we have 123456 We have six elements and hands six branches and as far as North are concerned. Let's put doors on these north, which are not the simple Nords wherever more than two elements are connecting. So this is a simple North. This is not a simple Nord, and that's the only simple Lord, and let's also label them nor a B C and de so a loop is a close part in a circuit so that no Nord is crossed more than once. So basically what we do is we start from one Nord. We can start with any random north, and then we have to go either clockwise direction or anti clockwise and move in. Ah, lost fresh and so that we keep crossing different elements until Berries back to the same north we started from. For example, let's choose this North Aid. That is where we start from. So if we go in this fashion a law across extrude than across X three, then across X one, we're back to the original North. So that is one closed part, so that would be one loop. So in this fashion we can keep counting the different number off loops. So let's Nord on. How many loops do we get? And, ah, let's start with the you know x two x three x one or for the same loop. We can start with this point. You know, we can first cross x one, then x two and X tree. We can even start from here, okay, And that would mean x three x one and x two, or yet weaken further go anti clockwise direction. But let's start from here. So this smaller clothes part it would be x two x three x one in the clockwise direction, x two x three x one or even if we write it as x one x two x three or x three x one x two As long as it is the same clothes part, it is the same loop. So there's the first loop. Then let's look at this smaller one. So if we start from X tree, then we go to x four. Then we go to x five and then back to Ex Tree. So this would be another close part. Less righted as x three x four x five x three x four x five that is the second lube, then for the last one. It is simpler because we are only two element, so we can neither write it as x five x x or x six x five. Either way, it is a complete closed part. So this writer x five x six So these are the three close parts, and then we can further combine to smaller parts to create a bigger part. For example, this first most part and second close part can be combined toe create a bigger one. But in that case, we will have to ignore X tree. So if we start from here, go to x two x four x five and then back to X one. Yeah, that is yet another close pot. So there's writer as x one x two x four x five and back to x one x one x two x four x five So that is our loop. Now let's combine this second loop and this third loop these two smaller ones to create a bigger loop And now we will have to skip x five. So if we write it as x three x four x six and then back to work three so x three x four x six. So there is another loop and lastly, we can combine all these three to create the biggest loop. And in that case, we will have to ignore extra and X five. So this bigger loop biggest loop would be x one x two x four x six and then back. So next one X do X for an X six. One thing you need to know down here is you cannot combine this loop in this loop because they're not adjustment. Okay, so they're separated with this loop so we cannot combine these first and third look. So, in total, we have game with six loops. 123456 Now let's see how Maney measures do we get as per this definition and a mash is a loop that contains no other loop inside that. So as far as Leuffer concerned, we were able to combine this smaller loop with the bigger loop to create yet another loop. But we cannot do this in case off measures. So if I write, how many measures do we have? We can only consider the smallest loops. Okay, the loose which don't have any other loop inside. So the 1st 1 The first loop is a mash x one x two x three x one x two x three and remember this one and x two x T x one These are exactly same. We are only starting from different positions, but we're reaching back to the same position where we started from. So this one and this one is exactly the same mesh and saying, Look, then here is another smallest loop. So we can write to the x three x four x five x three x four x five, which is same as this second group. And then here This is another smallest look so x five and x six. This is also a mesh. There are a total off six loops part out off those six loop only the 1st 3 R D mesh is the remaining ones were the bigger loops, which had some other loop inside that so that does not qualify for being a mesh. So based on this criteria can also say that every match is a lube. But not every loop is a mesh. So all of these measures are lose in their own right. But not all these lose our measures, only some off them, which are the smallest loops. These can be called measures for Hope. This clarifies the concept off loops and meshes, and what is the major difference between them? So thanks for watching and see you in the next lesson. 29. 216 All about Series and Parallel Connections: welcome back in this lesson. We're going to look at two extremely extremely important concerts when it comes to understanding and analysing circuits. And these concepts are called series connection and parallel connection. So first, let's look at what a series connection looks like. Two elements are said to be in Siris if they share a simple Nord and here the emphasis is on sharing a simple note. Okay, so this is what a serious connection looks like in here. We're assuming that this X one next to this connection is a part off a bigger network where this point at this point, they're not connected to each other electrically. So x one and X two are only connected to a simple Nord. And then we can see that X one and x two are in Siris with each other. So elements in Siris share the same current. Why is that? Because imagine if a current I was entering X one, then the same current leaves x one. And when it comes to entering X two, there is only a single part for current. So all of that current coming out off X one has to enter extrude ok, Similarly, the same current has to exit extra as well. So the incoming current and the outgoing current and the current in between all of them are exactly the same, even if you have more than two elements connected in series where X one and X two are in cities with each other, X two and X three are in series with each other. So again here you can see that the current entering this all of that has to leave this and then enter into the next element than all of them. All of that current has to leave extrude than enter extremely and so on. So the incoming current at the start off this series connection would be exactly same as the current leaving this CDs connection because to our we have only a single part for the current to flow. The next type of connection is apart. A little connection. Two elements are said to be connected in parallel if they share the same pair off north. And here you see, for serious we only had to share a simple nor But here we have to share the same bear off north. And here is an example where X one and X two are sharing the upper north as well as they're sharing the lower road. And please also note down these doors, which means that this is not an independent circuit, but it is a part off a bigger network, which we cannot see. But we can only look at X one and x two whenever you have two or more elements connected in such a way that they are sharing the same Pierre off north than we would call them connected in parallel. So the elements connected in parallel shared the same voltage. And the reason is, imagine if you had some voltage. We won across one of thes elements. Then from our knowledge off north, we know that the potential at this point is same ads as the potential at all other points on this note because they're connected toe uninterrupted wires. So this potential appears here as well. Similarly, this negative potential appears here as well. So as a result, the same voltage appears on the other element in this battle network. Sorry, this has to be the same voltage as this one like ways we could have more than two elements connected in parallel. For example, if I extend this, I can connect as many elements inside in between these two terminals, and all of them would be called to be connected in parallel. So if this is extremely, this is X four and so on. All of them are shooting the same nor so same pair off north, and hence we would call them being in battle, and all of them would have the same bolted across there. So I hope the concept off parallel and series connections is clear. If you still have any questions or confusions, just post your questions in the Q and A section, and I would love to further clarify this to you. Thank you for watching and see you in the next lesson. 30. 217 Example of Series and Parallel Connections: Let's do a quick example to dust your understanding, off series and barrel connections. So here we have the same old circuit and we're as to find which ones which elements are connected in series and which ones are connected in parallel. And as a reminder here, I have written down the criteria for CDs that the elements have to share a simple nor and for barrel. They have to share the same beer off yours. So we will start off with ah mentioning which north do we have? So first off all, let me mention this as north A this Nord as B. This is another Nord colored sea and this and this their part off the same north. So let's call it deep. So what do you think? Which limits are connected in series? The simplest way is to sport which off the north is the symbol north, So B. C. Indeed, these are definitely north, A simple nor is because they're connecting three or more elements. So the only simple nor we have is a So the elements which are in Siris are going to be on both sides off the simple note. So the element X one and x two They share a simple Nord So the only elements in cities are X one and x two On the other hand, which off the elements are sharing the same bear off north. Well, um X four X two x tree. They are only sharing a single nor, ah, there is only X five and X six which shared the same pair off north. So expire next six Their upper north is see and ah there lower Nord is deep. So yes, X fire and X six They're definitely in bell Now a bigger might be tempted to also say that X three is also in parallel with ex fire and XX But that would be wrong because X tree has this Norby while X Fire and XX are sharing North Sea which is different from B and they're separated through this element x four. However, if there was no X for and this this nor this nor there were connected through a continues wire without any element in between. Then yes, we would say that x three x fire next six are in parallel. But under the current scenario, only X fire and x six are in power. So in the next lesson, let's do another example about sees barrel and all the other concepts we have learned. 31. 218 EXAMPLE: Welcome back. Here is another chance to revise some off the important concepts from the last few lessons . So we're given with this network where we have six agreements x 12345 and six and were asked to identify all the north and the circuit. All the simple North loops measures all the elements in Siris and all those elements which are in balance. So we will start off with looking at how many north we have So you can see this is the first Nord. So let's call it a then. This is the second Nord. Let's call it be you can, you know, name them in any sequence. It doesn't matter. There is 1/3 north. Let's call it see and hear this big Nord less collard D. So in total we have four north and let's write it down here A, B, C and the These are the four North we have out of all these north. Which ones are simple north? Well, for simple north, there have to be a maximum off two elements connected, so B C indeed, these air definitely north. Simple north. The only simple nor weaken sport here is North A because it only connects X one and x two. So the simple Nord we have is a Now let's look at how many loops we have, and this is going to be a little bit lengthy. You can see that all the closed parts in a circuit are loops, so let's start with this upper most close part. Basically, we have to start from any Nord part. Then we need to go in either clockwise or anti clockwise direction and keep going in a close part until we come back to the same old North. So if we start from Norby and if you go into the clockwise direction, we have x one x two x four and extra and then we're back to Norby. So for simplicity, let's skip these X and let's only write the sub scripts. So 1 to 4 and three So one toe four and three. This is our first loop, and once you decide whether to go in clockwise direction or anti clockwise direction, it's a good idea to stick to that same direction. Through are the problem. So here we went in the clockwise direction. Let's also go here in the clockwise direction as well, so we can start with either this point at this point at this point. So let's start with this x three x 16 x five. So 365 would be our next loop 365 Similarly, this is another close part. So it has only do animals, so let's write it for in six. So these are the small loops, and now we can combine the sets off to lose to make bigger loops. So let's combine this upper loop and the lower left loop first. And to make it further simpler, I will use different colors. Now if we don't start from this element and if we keep going, then instead of going to extra if we go down so as to use the lower loop. Then in doing so, we have to skip X three so we can start from X one. Let's say so. 1246 and 51 toe for six and five. I hope you can see that. So that is our fourth lube and left in the color for the next one. We can use this upper loop and the lower right loop this time so we will keep going in this direction. And from here we will come back. And in doing so, we're skipping X 41 do six and three, 1 to 6 and three. Now we can skip the upper loop, and now we can combine the lower two loops. So if I again, she is the color that's used the screen one. So now we can simply go in this freshen. So we start with three, go to four, then back to five and then back to three. So in doing so, we escaped six. So 34 and five, 34 and five. And so far we have 123456 loops. And in the end, we can combine all these three loops to make the biggest loop. So if we go from X one toe X two and then Goto x five, then back to X one. So in doing so, we skipped x 34 and six, one, two and five. We have total off seven loops. And now we were able to consider all the possible piers off these loops because all of the's are connected to each other. And now we can come back to the same old color. Know which ones off? These are measures well, as but the definition measures are the smallest loops, which don't have any other loop inside. So such kind off loops are this upper loop, the lower left and the lower right. And these are actually the 1st 3 loops that we came up with. So 1 to 4 and three let's write them here again. 1 to 4 and three, then 36 and five, 36 and five. And, uh, this 16 and four or four and six. So out off all the seven lose the 1st 3 the smallest ones. These are also the measures, and the next question is which elements are connected in Siris. So the simplest way to support the elements connected in series is to look for the simple nodes. And in this whole network, we only have a simple, single simple North, which is, nor it the elements on either side off the Simple North are going to be connected in series because they are sharing that simple north. So in this network we only have two elements which are connected in cities, and these are X one and x two So x one and x two These are elements connected in series. Four elements connected in barrel. We have to look for elements which hear the same bear off north now. Ex fire next six there north sharing the same beer off north, although their lower nor the same but the upper north are different, which are separated by ex tree, so expire next six is definitely Northey answer. Similarly doing for they have only one nor common. The other north is different. Same goes for X one and X tree. So the only two elements which are connected in parallel are X four and x six. Because you can see this side off. Both these elements is connected to North Sea and their other ends are connected to Nord de . So they're sharing the same pair off north, which is North Sea and ignored be so the only elements in parallel r x for and x six. So I hope this little exercise was helpful for you to further understand the concepts off North, Simple North loops and measures in series and parallel. Thank you for watching and see you In another lesson 32. 219 Introduction to Kirchoff's Laws: know that we are aware off the relevant terminology. We are in pretty good shape to discuss Gourcuff's laws. These laws are named after a German physicist named Gustave Gorkov from the 19th century, the first law known as Gourcuff's current law Abbreviated as gay CEO. This establishes a relationship between all brands currents associated with a node, while this second law known as Dickov's Walters Law or Gabriel for short, This establishes a relationship between all brands. Voltage is associated with a loop or a mash. What off? These laws are based on the principles off charge, conservation and energy conservation. Let's now look at each of these laws in Dedeaux. 33. 220 Kirchoff's Current Law (KCL): in this lesson, we will talk about the good golf's current law, also abbreviated as guests here. So consider the bronze currents associated with a Nord end at any time. Some off these currents flow into the north and other currents flow out off the note. So as per k c. L at any time the some off all the currents entering this Nord must equal the sum of all currents leaving the note. So that is the statement off a seal. And mathematically, we can write it in the form off this question where you can see this sign means submission . So here on the left side, we have sigma off. I the current going inside this nor so on the left. It means that some off all the currents going into this north end that is equal to this term on the right hand side, which means that some off all the cars going out off this north end in simple words, it means that charge must be conserved and a north cannot accumulate or eliminate charges. Or we could also say that the total charge flowing into the north must equal the total charge throwing out off the note and expressing the flu off charges in terms off current were the yield. Guess you. The concept off a Nord is similar to the concept off a junction where multiple water pipes connect. As you can imagine, the amount off water entering the junction must equal the amount off water leaving the junction. So that's a nice enology between the flow of water and the flu off charges, which is also called current. 34. 221 EXAMPLE of KCL: Welcome back knowledge tried toe. Apply our understanding off Google's current law on this diagram. So this is the same diagram we have bean looking at before with six elements. So let's first off all label all the north. So this is going to be north. A. Let's call this Norby Nord see Nord de, and this is going to be another dot not a very first step whilst hollering. Any problem using case yellow is that we need to mention all the bridge currents along with their directions. And if you don't know the directions off the currents, we can assume any direction. Okay, so here we don't know the directions off these current. So let's assume that this current through the first element is flowing upwards. And since this subscript is one, let's call this I won. This is element. Do so. Let's assume its current is flowing towards right with the name I, too. This is Element three. Solar's collards Guard I three. Let's call this current I four and let's assume X flows towards the right. Then I five and I six, let's assume board flu downwards and call them I five and I six, respectively, No, we can write down the equations off Casey L for each off the north. So let's start with Nord A, which is the simplest one. So the question for North a would be you remember There are three different forms off Casey immigration. So let's use the 1st 1 where we ride currents and during the north on one side and currents leaving the north on the other side. So for north a the current and drink this north is I won and current leaving is I two says there are only two currents on the left side would have by one that is the current entering that is equal toe I toe which is the current living for north be We have three currents So I do is entering and I tree and I for both are leaving so entering current on one side I do and the some off leaving currents on the other side So I three plus i for by three bless I for then for North Sea again we have three elements Eso i four is entering I five and I six are leaving So for North Sea I four is entering and I five or 96 are leaving I five bless I six and lastly for Nord de. You can see that nor D has four elements connected to that I three i for Sorry, I three I five and I six. All of these are entering this north. I three bless I five plus I six is equal to and the leaving guarantee is only a single guard, which is I won. So that is how we can write the guests. The immigrations for each off the North's In this process, finding a current means finding its magnitude as well as its direction. And here we arbitrarily assumed all the directions for currents. If we were given some solid numbers, then we would first do all the calculations. And at the end of the calculations, if the value for a current turns out to be positive, that means our assumed direction for that guarantee was correct. On the other hand, if the value for a current turns out to be negative than that would be in the current actually flows in the direction opposite to our assumed direction. To rectify that, we would reverse the arrow on the diagram and devalue off the current becomes positive. Now let's look at this scenario. Where for Norby were given some actual numbers. So again, for Norby, the question was the current entering North, which is I do that is equal toe I tree plus I for So I Do It goes toe I three plus I four and this is not equal to sign. Were just riding the question for Norby. Now, since we know the values where I do and I three, let's put them into this equation. I two is five ampere five Impair is equal toe I three, which is to in Piers Plus I four, which is unknown. Nor to solve this equation. We would place I four on one side, and everything else would go on the other side. So to impairs goes to the other side. It becomes minus two impairs so this implies I four equals to five amperes minus to em peers. And that turns out to be three m piers. So, as we said before, if after the calculations devalue for a current turns out to be positive, which in this case is I for then that means that the original assume value for the current was correct. So this is three impairs so we can simply write it as three m piers And now you compared these values It makes perfect sense because five ampere is ending this Nord. And from here you impairs is leaving. And here three impairs is leaving. So a total of five amperes is being divided into three impairs and to impairs knowledge look at another scenario where we're still talking about the North. Be part In this case the values are a little different. So for north be again The question was I doing goes toe I three i three plus I for now we can put in the values I do is six ampere I treat this time is seven and Pierre plus I For now. If we solve for I four, we get six impair minus seven peers which turns out to be minus one appear So what do we do when the current turns out to be negative? Well, in this case we can say that minus one ampere is flowing towards right. However, it is not very intuitive. So instead we reverse this sign and also video Worster direction off this current so instead off writing this, which is not the preferable way. We reversed the direction off current and we ride I for equals two instead of minus one. Now, since we have reversed the direction off current, we would call it plus one and beer. So coming out with negative really, for the current means that our original exemption for the direction off current was incorrect. So we have to reverse it. And now, if you compared the relative magnitudes off the currents from this side, six empire is entering Norby, and from this side one and Berries entering north P. So the total current entering is six plus one impairs, and that is equal to seven in pairs. Now, if you look at the leaving current, it is also seven peers, so that makes perfect sense. So that is how we can interpret the reserve off current calculation if it turns out to be positive or negative. Thanks for watching and see you in the next lesson. 35. 222 Other forms of KCL: welcome back. In addition to deform off K C. L. We have just started K. C. L can also be expressed into other forms where we can either assume that all currents associated with the north flow into the north or their flowing out off the north. In either case, once we do the calculations, at least one off the current values will have to come out to be negative in order to satisfy the charge conservation principle Knowledge. Look at these two other forms off KCIA. So the second form off K C l is this sigma and I n minus sigma and I out equals 20 And if you compare this first form with the second form, all we did was we took this term on the right side and we wrote it on the left side after the first term. So the second term is being subjected and on the right side we have zero as but this equation, we can say that at any instant, the algebraic sum off all the currents associated with the Nord must be zero where the entering currents are taken as positive and leaving currents are taken as a negative However, since it is just a rearrangement off the other equation, of course it will yield the same result as the first question. So these are the first and second form off the GCL and the third form is this So that is Sigma and I out minor sigma and I n equals 20 So all we did was we wrote this second form in the reverse order. So here we have the in term first. Here we have the out term first, So it is the same as the other two equations, except that now we are regarding the living currents as positive and the entering currents as negative. But the reserves will be exactly the same, irrespective off which off these three forms off case yell you use in your calculations. No, the question is which one off these three forms is more preferable or which one you should use more well. The first form is more intuitive as all currents appear in the positive form, so there is a less chance of confusion. You do positive and negative signs. However, the other two forms can be more helpful in certain scenarios. For example, while doing nordle analysis, as we see later in the course, but overall, it doesn't really matter which form off facial equation you use as long as you applied correctly. 36. 223 Kirchoff's Voltage Law (KVL): Welcome back. We have already talked about Casey L. And now we're ready to talk about Kirk of Second Law, which is known as the Kickoffs Voltage Law or Cavey El for short. So consider the branch world is is associated with a given loop L As we go around that loop , each branch voltage may appear either as a voltage rise or voltage drop. For example, let's look at this situation. Offer an electric circuit there. This is a small portion off a bigger circuit. So what these girls on the edges means that the circuit continues on the left side as well as on the right side. So if you focus on this loop where we have no A and Norby, then let's say we know the values for Nord A riches to work and devoted for no b is five world. So if we go around this loop in the clockwise direction, then first we will see north a and then Norby. No. In this case, Norby has higher voltage than North s. So we put a plus sign towards Norby and negative signed words nor a because plus sign has higher voltage than the negative one. now going from north a Do not be. We see a three worlds voltage rise because we are moving from a Nordoff lower Walters to a Nordoff higher voltage. So this one is going to be world. His rise. On the other hand, let's say that instead off two worlds, let's say that we know this world is to be it would we is equal to eight words and let's say that we knew we be equals three words. Now the situation has totally changed because now the voltage at Nord, its creator and Norby has a lower worded. So we will put a plus sign towards North A and a negative sign towards Norby. And with these values, if you go from north air to not be we see a voltage drop. So that is what is meant by voltage rises and voltage drops in a loop. Now the process voltages around a loop are always going to obey the following law. It says the some off all the voltage rises around the loop must equal the sum of all the voltage drops around that group. And here is its mathematical representation. On the left side, we have Sigma L Boulders rice, which means the some off all the voltage rises around the loop l and that is equal to Sigma l World is drop, which means that the sum of all the world is drops around the loop. So that is gurgles voltage law known as Gabriel. 37. 224 EXAMPLE of KVL: knowledge tried to apply gave you on this diagram. The first step is to mention all the print voltages in a given loop, along with their polarity, just like in case yell very assumed directions off unknown currents in the beginning. Here we will have to assume polarities off all the unknown voltages. So let's say that we come up with these assumptions for the voltages. Eso for all the Vertical Cos. X 135 and six. I have assumed their positive terminals to be the upper one, and the lower terminals are taken as negative. And for the horizontal components, let's assume they're right. Terminals are negative and the left terminals are positive. So let's go with this assumption. And now we need to write the Gabriel equation for each off the loops. This is the first loop, second loop, third Luke. And then we can combine de Beers off a Justin Loops, so this would be the fourth loop. This could be the fifth loop, and then if we combine all three, then this would be the sixth loops. Overall, we have six loops and let's first right down the loops. So 1st 1 is X one x two and x three x one x two x three This is our first loop. The second loop is extremely x four x five The turn loop is x five x six x five x six and now let's combine the first and second loop to make the fourth lube x one x two x four x five. Similarly, if we combine 1st 2nd and third loop x one x two x four and x six x one x two x four x six This is our fifth law. And for the last one, we can combine this second and third loop So that becomes x three x four x six x three x four x six. So there is just how I am writing the loops. You may write them in a different sequence, but overall, there are a total off six loops. No for each of the loops we need to ride. The voltage rises on one side and the voltage drops on the other side. Let's assume that we are going to go in the clockwise direction for all these loops. Okay, now it's totally your choice. But let's assume this clockwise direction and less write down the equations. So for X one, if we go in the clockwise direction Here we go from negative terminal toe positive terminal which is a world is rice then for veto. It turns out to be from positive to negative which is a world is drop similarly for V three . We go from positive to negative which is a voltage drop. So there is one voltage rise which is We won. We write it on one side. The other tools are worth is drops. So we do and Vetri. Our work is drops. We write them here on the other side. We do plus we three, which is the some off world is drops in this group for the second loop again we go in the clockwise direction So we three turns out to be worded Rice before and we five turn out to be worthless drop. So we three goes on one side that is equal to the two Wolters drops added together before and V five before plus B five then for the last one again going in the same direction x five Sorry V five is from negative to positive. It is voltage rise And there is another world days which is from positive to negative in clockwise direction and that is a voltage drop. So we six on the other side. No. Four x one x two x four and x fired 124 and five If we again going to evil days are in the clockwise direction. We see X one as voltage Sorry V one as or did rise we do before envy Fire are all voltage drops so they will be together. We do before and be five We do plus B for plus B five for X one do for in six which is the biggest loop again we have only one voters rise we want and voltage drops are due for and six we won because toe we do plus we for plus we six And lastly for the three before and V six We three is a voltage rise. We three is a voltage dries and before and V six our world is drops x three x four and next six Yes, you have dual drops and one world age writes So these six secretions are all when we go in the clockwise direction clockwise and clockwise now The question is what happens if we go in the anti clockwise direction? How are these equations going to change? Well, going in the opposite direction? Of course, the voltage rises will appear as Walter's drop and wise worser. So let's look at the first loop going in the counter clockwise direction this way. So let's cross our the first direction and let's go in the counter clockwise direction. So see what happens toe question and we will only look at the first loop and we can extend that concept for all the other loops. So this time you see, we go from negative to positive for Vetri, so it appears as a voltage rise. Similarly, we do. We go from negative to positive. So again it is a voltage rise. But we won here. Now we go from positive to negative. It's a voltage drop. So what? Age rises first we do, plus we three. We do. Plus we pre that is the sum of voltage rises is equal to the sum of wordage drops. There's only one world is drop, which is we won. So that would be the new aggression for the first loop. And if we compare this one with the original equation you see bought equations are exactly the same. The only difference is the previously left hand side has now become the right hand side, and the previous writer inside has now become the new left inside. That is the only difference. But overall, the question is exactly the same. So again, going either in the cloak ways are counterclockwise direction to cover. The loop does not make any difference. Of course, as long as the same direction is followed through are the loop Now, since Walters is a directional quantity, we need to find both the magnitude and polarity for each unknown voltage, just like a CEO in gov. LV, assume polarity off unknown voltages and then use Gabriel toe find the unknown work it. And as a result, off our calculations, a positive voltage means are assumed. Polarity was correct, and a negative result means that the actual polarity is opposite. So what we had assumed and direct if I that we would reverse its assumed polarity and to illustrate that, let's look at the same situation once more and let's write down the equation for Loop one, which is V one equals Toe B two plus we three. Now let's say that we know to off these voltages the 1st 1 Let's say we know this Toby plus Nine World and this one. Let's say we know this to be six world and we want to find out v two. So Asper the equation we do it caused 31 minus we three. And if you put these values we want equals Tau nine world minus, we three equals 26 world. So it turns out to be nine world minus six whole days. Three. World. Now, as a result, off our calculations, this unknown voltage, its value turns out to be positive. Which means that our originally assumed polarity for Vito is correct and we can simply write it down as we do equals 23 World. On the other hand, let's assume that now we want we know this as four words and Vetri as Six World. So with these values, if it tried toe, find out, we do. We won. Here is four words Let's put in the value minus retrieve ages six world. So this one in this case turns out to be minus to work. So if such a situation occurs where, as a result off your Kerviel calculation, the unknown voltage value turns out to be negative. Well, in that case, what you're going to do is you're either going to write this. We do as minus toward with the originally assumed polarity or a more preferable way would be toe reverse. This polarity, the originally assumed polarity, was positive here. But if we reverse it, the positive would be the other criminal and the negative terminal. The positive becomes negative. The negative becomes positive. And with this reverse polarity, now we can write veto as to ward. So again, if you do the calculations off Carrie L. And the unknown voltage turns out to be positive, that means you're originally assumed cultish polarity was correct. On the other hand, if you're result turns out to be negative, that means you need to reverse the really assumed polarity off that for debt. And you need to make the sign off your calculation positive. So that is how you solve, give you'll equations and interpret their results. So I hope this makes sense. And thanks for watching. I will see you in the next lesson. 38. 225 Other forms of KVL: Welcome back. We have already looked at the original form off Gabriel, which goes like this. The summer voltage rises in a loop is equal to the sum of Fortis drops in a loop. But just like in case seal, Gabriel also has to alternate forms. And the second form off Gabriel goes like this. The some off voltage rises in a loop minus the sum off worlders drops in that loop is equal to zero. So this equation states that at any given time the algebraic sum off all the prints wall Tages around the loop must be zero where voltage rises are taken as positive and voltage drops are taken as negative. And the third form off Gabriel goes like this. The some off voltage drops in a loop. Miners, the some off voltage rises in that loop is equal to zero. And in this case, world is rises are being taken as a negative and voltage drops are taken as positive. So that is why what? These drops are represented first in the question and voltage rises are written later. Similarly, in the second case, where we are taking voltage rises as positive we ride voltage rises first and work is drops which are taken as negative. We write them in the second term. However, just like in case off Casey L any off these three forms off gave e l can be used to achieve the exactly same results. And let me try toe Illustrate that with the help off this first loop which is a portion off the diagram we saw in the previous lesson. So these symbols mean that this diagram continues on the right, but we are only looking at the first loop. So let's assume we're going toe going in the clockwise direction in this loop. And now let's write down the equations for this loop using the first form second, former third form and then compare them. So ask for the first form. World is rises, go on one side and voltage drops go on the other side. So in the clockwise direction, there is only one voltage rise which is we won. There is equal to the sum of voltage drops which are we do and re three. So we two plus we pre This is the equation as but the first form. Now let's try it right The same equation using the second form. So here will digitizes go first. So there is only 11 world his rise, which is 31 minus the some off voltage drops. So now there are two words drops we do in VT. And we need to write them in bracket. So we two plus we three some of what is rises minus some of world's drops is equal to zero . No, Either we can open this Packard so both of these voltages would become negative. And then if we bring both these to the other side, they would become positive. Or we can simply do that in the same step. Even is equal to this whole negative term in the bracket can go on the other side and it will become positive. So it would become We do bless we three. And if we compare it with the original question we wanted was to be two. Plus we three. It is the exact same question. Similarly, if we write the Lubick question using this third form here, voltage drops go first. So the summer voltage drops we do in Vetri, we write them first. We do. Plus we three miners. The sum of wordage rises. There is only one voltage rise, so minus B one equals 20 Now we want can go on the other side to become positive. So this takes the form off. We do. Plus B three equals two we want. And if we compared with the 1st 2 equations, it is exactly the same. The only thing is it's left and right and sides are swift. But overall the aggression is still the same. So this confirms that all these three forms off Gabriel year the exact same result. Now, the most important thing to remember while applying either give e l or Casey away is starred. Current has a value as well as a direction. Similarly world. It has a value as well as a polarity. So just to emphasize that I have underlined these two words, so always direction is going to be related to current and polarity is going to be related to voltage. Hence, we must be very careful with the signs off Voltages and currents as carelessness with their signs is one of the most frequent causes off errors in the problems related to circuit analysis. So with that, we can conclude the Gergiev's current and world is loss 39. 226 EXAMPLE of using Ohm's and Kirchoff's Laws to Solve Circuits: hi and welcome back. So far we have solved many example problems in this course which required knowledge off just a single law or principle. But here is an example where we would need knowledge off multiple laws. More specifically, we're going to need the knowledge off homes law as well as gives laws to solve this problem . Now, in this question there two parts. The first part is find the value off my Nord in this circuit. Now this I Nord and its direction, it is given to us and were asked to find its value in this Cuban direction. That is why I have drawn this in blue. And the second part says that test your reserve off first part by verifying power conservation in the circuit. Now what power conservation means is that within a single circuit, the total power consumed must equal the total power generated. So that is the law of conservation off power. And if our reserve from the first part is correct, then if we calculate depart, generated and participated both off them are going to be exactly the same. So let's start solving this problem now to solve any circuits problem. It's a great idea. Toe briefly. Look at the circuit, how the connections are made and how the elements are going toe work with each other instead of just blindly jumping into starting the solution. So here I have laboured thes north. First of all, we have three north. The north is simple north and then Norby and North Sea are not simple lords. Then North sea. I have grounded this and right away We can do some basic labeling on this diagram and then we can see how many variables do we need to solve this problem? First of all, since North Sea is grounded and 1 20 wards is negative, terminal is connected to North Sea and Nord is connected to positive terminal. The north is going to be exactly equal to 1 20 Ward 1 20 ward And since one during the warden, 10 homes. These are connected in series. So this fine art is again going to be passing through this currents this world his horse as well. Now this I Nord is given to us in this current direction. So we can also labeled the voltage across this resistor. Ah, in the seam color plus minus since I noticed going through this resistor. So why not label this world it as we not as well and ah, this world it across 50 homes resistor I have just assumed its polarity that it is positive at the top of negative at the bottom and accordingly, since we one is devoted across the resistor, its current going through the resistor downwards, let's level it as I want. Now one thing is clear that for resistance is if we know their value, the value of the resistor and either the voltage or current than the other quantity can easily be found because homes losses that for resistor, uh, is equal to i r. So if we know any do off these values for a resistor, we can easily find the 3rd 1 Now the value for resistor is known. So if we know the current I one finding we want, it's simply a matter off multiplying the current and resistance. Now, since we need to verify the power conservation in the circuit, we need to find all the voltages and current in the circuit. Just I think finding the value for Northern I one would be enough because based on that we confined we Nord, we confined we one and then we applied the power conservation principle. So basically the only unknowns here we have as I Norton I won. And from the help off in Northern Ireland we can easily find the north. And we want so to find I Norton I one we need to different independent questions that both contain I north and I want variables. Now let's try to look like your gifts. Current law involved his law in this diagram to get two equations with both carry in northern I want so First of all, if we apply K c l on this nor a it is not going to help because the current minority is going through the same old the source as well as the resistor so that I know that equation won't help us finding I not No, let's apply. Guess yell at Nord Be What are we going to get? Well, let's apply the first form of kiss yell which is the sum of currents Entering a Nord is equal to the sum of currents leaving the north. Now I know it is entering this Nord and six Impair is also entering this north and the only living parent is I want so current The sum of currents entering I Nord plus six is equal to I one. Now here I am neglecting the units because I assumed that all the currents are in in piers so we don't need to write in peer here. So let's call this question one. So we're already applied gcl And now let's see if we can take benefit off Gay Viel if we apply giv e l in this loop where we have 50 on resistor and six impair current, it is not going to help because these two elements are in parallel so de voltage across 50 ohm and six MP resistor. The voltage for both element is going to be re one. So if we apply the Gabriel, it is not going to help us because we won't get inordinate. I want in that equation. However, if we apply gave you on this first loop with these two, resistance is and the world is horse. We are definitely going to benefit from that. So kbl in Let's call it Loop one. Now let's use the first form off gave yell which says the summer voltage rises in a loop is equal to the sum of voltage drops in a loop. Now let's look at this. Gave yell in the clockwise direction. You see, we not and we won both our voltage drops. The only world is rises 1 20 world. So the sum of voltage drops is there is only one world days 1 20 I'm not going to write world because we assume all the units are in force. And uh, let's write this drop The first drop we Nord bless. We won Now we actually needed this equation to also contain I. Norton I one How about if we write This world is in terms off the current Einar and 10 on resistor Because this is for resistor so we can apply homes law for both these resistors. So we get 1 20 is equal to We know it is equal toe Leinart times Then then I Nord Plus we one is equal to 50 I want as per owns law 50. I won. Now let's put the value of I want from Equation one into question toe where this is our second question putting one into toe we get 1 20 because toe and I Nord bless 50 i one is equal. Do I not bless? Six I Nord plus six. Now I can simply solve this whole equation in one step but just for clarity For those who are not very familiar with solving simultaneous equations, I'm going to go step by step so we get 1 20 equals toe Te Ni Nord. Let's multiply these these things in the bracket 50 times I not as he called to 50 i nord plus 50 times six is 300 now let's solve this 50 i nor plus 6 10 I nor physical do 60 i Nord equals to one drink T minus 300 is minus 1 80 So this implies I not because to minus 1 80/60 equals two minus three And since this a guard it is in in piers So that waas what we were looking for And let's also put this sign our institution one. So this implies I one equals two i Nord, which is minus three and bear plus six and beer. So six minus three years three m beer. So with that, we have already soared the first part there. I know it turns out to be minus three impairs in this direction. OK, going to the right. This Einar is equal to minus three in peer Since this waas given in the question So we have conserved this direction But we can also write it by reversing the direction off this current. We can call it a prion peer current. The North was in this direction so we write it as I know it because toe minus three impaired there is the solution. But just to label are diagram correctly, we can write it as plus three impairs going in the opposite direction and resultant Lee. Since resistor always disappears power, the current goes from positive to negative terminal. So this is going to be wordage across 10 ohm resistor with this bullet Now, the second part is test result by verifying power conservation in the circuit Now therefore elements in the circuit there two resistors. So for resisters, there is absolutely no confusion. We know that resistors are always always always going toe disappeared power. A resistor would never generate power but forwarded sources and current sources Sometimes what did sources may generate power sometimes they made dissipate power. But overall, in any given circuit, that has to be at least one element that has to be generating power. And there has to be at least one element that has to be dissipating power. So for these toward his horses, at least one of them has to be generating power. Maybe both of them are. By the end of the our calculations, we would know definitely. But right away I can tell that at least one of these sources is going to generate power. And at Max, only one of thes sources is going to dissipate power. So let's label this correctly. This is three m beer and this is also three m beer. No, I'm going toe stick to this current direction because the first part has already been done . So now we're off to the second part. Now, just as a reminder about passive sign convention. We know that if power is being dissipated, its sign is going to be positive, and current always flows from positive to negative terminal. Similarly, in the case off power generation, the sign off the power is going to be negative and the current is always going to flow from negative to positive terminal. So let's start with power dissipation. The simplest case is for the two resistors we know they are definitely dissipating power. So let's compute the power for first resistor. It is 10 home so power for 10 home now to calculate powerful resistor. There are three formulas Either we can multiply its current and voltage are I scare are or also be scared over our whichever is simpler in terms of calculation, we can use that now for this resistor. We know that government three impair current is flowing towards the left So the current has to be flowing from positive to negative terminal because it is a dissipation case. So since we already know or scattered and we already Nords resistor so the simplest case would be we can put the values here current is three ampere. Even if we look into a guard, the original direction for current where it is monastery impairs Even if we put it in this equation, you know that current is being scared. So whether it was by the three or plus tree, it's going to be taken as nine and this negative sign off current is not going to make any difference. So three scared times are which is then So nine times 10 is 90 Ward and since this is the case off participation, the sign of power is going to be positive. Then let's look at the power for the 50 owns resistor and again for this resistor. We also know if Scotland, which is three amperes so we can simply apply ice care, are where I is. Three your scare times 50 So nine times 50 is for 50 Ward. That is the second power dissipation and now we can see rather the world, its source and the current source are generating power or disappeared power and we can simply determine this by visual inspection. Now you can see this three amperes current with a positive sign. It is going down which is in the direction off, positive to negative. And from here you can see that when current flows from positive to negative terminal, it is the case off power dissipation. I'll simply right dissipation. And similarly, let's also categorized this current source whether it is dissipating or turning power. Now look at these six and their current sores and 50 board 50 home resistor. Both of these are in parallel. So do tell whether this current sources generating power or dissipating power we need to know the polarity across its terminals and the polarity for current source is going to be seen. As for this 15 resistor, because these are bought in parallel now, since we know that there is three impair current flowing down through this 50 owns resistor and the resistor is dissipating power. So it's positive Terminal has to be the upper terminal and the Lord terminal has to be negative. And because the six amperes current source is also in parallel, so it's upper terminal has to be positive and lower terminal has to be negative. Now we can look at the current in current source. It is going from negative terminal to positive criminal and here you can see that when current goes from negative to positive terminal, it is a case off power generation. So here we can write that it is generating power. Now let's complete the part off participation. The only element left is this worldly source So power off this 1 20 world source is equal to for the sources. There is only one power formula. It is we I we know the world age for this world is source. It is one printed board and the government for this world. The source is three and bear. It is same as the current internal resistor. So three ampere 1 20 times three years 3 60 Ward And it is going to be again depositor because the part is being dissipated now, Toto power dissipation is equal to some off these powers 90 90 plus for 50 plus 3 60 is equal to If you calculate that it turns out to be 900 Ward, was it different? So let's write it here in pressured 900 walked So that is the total participated and not the daughter. Part generator must be exactly the same. So let's do the calculation power generation. It is going to be pretty short solution because we only we know that there is only one and imagine ating power. So power off six amperes Current source is going to be world days, times current where it's voltages, same as the world to force a 50 ohm resistor. We're going to kill clear that in a minute But first let's write its current, which is six in peer. So we won the world for resistor is going to be equal. Do the current times. It's resistor, its resistance. So current is three impairs resistor is 50 homes toe on you multiply three with 50 we get its world is and that is going to be the same wordage across the current source. So pre I am 50 and when you multiply that three times 50 is 1 50 times six in piers which is 900 ward And since the current is flowing from negative to positive terminal, it is the case off power generation and that has a sign off Negative. So the power generated is going to be equal to minus 900. Now, looking at the total part generator in total power dissipated. We can say that both off them are equal in their magnitude so we can ride Well, we're generated equals to power disip Ettridge and hence hence verified. So basically we calculate discouraged in the first part and then very fired that by verifying the total power conservation in this circuit. So that is how we saw this problem by combining the knowledge from owns law as well as your coughs, voltage and current loss. Thank you for watching and see you in the next lesson. 40. 227 Circuits Containing Dependent Sources: hi and welcome back. Know that we know how to analyze simple electric circles using arms law and Kickoffs laws. The analysis off circuits using dependent sources is just as easy. And let's look at that with the help off this example where were asked to solve this circuit. Here you can see a dependent current source before writing any questions. It's always a good idea to examine the circuit diagram closely. This will help us identify the information that is known to us and the information we need to find out. It will also help us to devise a strategy for solving the circuit concisely using fewer calculations. As we saw in the previous example. Not every loop in the circuit is useful for the application off gave yell. And similarly, not every note is useful for the application off K C. L. A little bit off. Careful thinking about the problem in advance can help in choosing the most appropriate approach and the right analysis tools to solve given problem. And in this way, usually we can reduce the number and complexity off equations to be solved for a problem. So first of all, let me level this diagram with all the north and the unknown Voltages and currents So the lowest north north sea I have grounded it and made it zero here This is a simple nor we have called it nor a And we call this Nord Norby then for the five homes resistor in relation to its current I not we call it's Walters we not and similarly for this 20 owns resistor I have assumed its current is flowing downwards It is I want and the voltage across the resistor is we won accordingly. Now just by looking at this circuit, we know that we want can be easily found using homes law if we know the value for I want so let me right owns law for resistor means we equals two i r. Then another important observation about this current source which is in fact er dependent sores is that its value is five i Nord so its exact value can be found if we know the value for I not Okay, So when we multiply for this current with five, we get the value for this current source So basically all the unknowns in the circuit can be easily found out if we just know the values for I Nord and I want. And since these are two unknown variables, we need do independent equations containing I Norden I want so that we can solve for them. And then ultimately we can find all the unknowns in this circuit. Now, apart from owns law, we have do other tools which we can use to solve the Sickert Gabriel in which we right the questions off voltage around close parts. So off course, we can write the Gabriel equation for this first loop. But we also need to know down there, writing equation the give you a question for the second loop won't serve any meaningful purpose because see this resistor and this current source both her in parallel to If we right, it's gave you a question, then the voltage across both these elements is the same, and it is re one which is actually the value we're tryingto find. So applying Kerviel in the second loop won't be off any use. Now let's apply Kerviel in this first loop. So we write the voltage rises on one side and worked. It drops on the other side off the question So if we choose to go in the clockwise direction 500 volts is the world is rise And this we Nord and this we want both our voltage drops So what is rise is 500 worked his drop is we not which we condemn tickly right in terms off homes law. So it is five i, Nord five by Nord Plus we want which is 20. I won Quinn d I won. And let's call this equation one. Now we need one more equation with ah in Northern I want so as to solve them simultaneously . So what about if we apply K c l? And now let's look at this circuit If we apply guess yell at North A It won't be any useful because, you see, both of these elements are in Siris. So the current flowing through this world resources same as deterrent through this resistor . So that equation would only be caring, Einar. And in fact, it is not going to be off any value. If we write, give guess Yell at this. Uh, this Nord a On the other hand, if we apply, guess yell either at Norby or North Sea. It would be a completely new equation and it would be carrying both I north and I want. So that would be very helpful. So let's apply Case yell at Norby now The currents entering Norby R i Nord and five I not from this dependent source. So the daughter current emptying this north is I not bless five i Nord and that is equal to the total current leaving from this north which is the current I want I won and this as equation Duke. Now we can solve these two simultaneous equations to find values for I Norton I want. And then we confined values for re north and we want. And that will complete the solution for this circuit. Now from a question, do we can say that I want is equal to six I not if we are these two currents together and if we put that value off, I want into a question one. Then we get put in Do in one we get 500 because to five I Nord bless Grandy I want which is six. I note six I nor, and that is equal to 20 times six is 1 2120 plus five s 1 25 I Nord And from here we can ride I not because to 500 divided by 1 25 which is for in piers So I Nord equals two foreign piers. And based on that, we can write the values for I one equals two six I not six fine art is six times for which is 24 amperes. So that is the second unknown. Let's write on All the unknowns here is to stay organized I nord We found it to be foreign Piers I want we just found out This is 24 amperes So these are the unknowns in terms off current. This is Ah five I not so five Fine art is of course, 20 impairs and these are all the unknown currents and similarly we won. Finding we want is simply a matter off multiplying this I one and 20 homes. So we one is 20 times 24 20 times 24 equals two for 80 world and we Nord That is this whole days And that is equal to this current Einar Times five where I notice four so four times five years, 20 world Now we can go ahead and level all the unknowns on this diagram. I notice he could do for years. I one equals two 24 amperes and five I Nord. We know that it is going to be brandy and beers. Then we note we just found out it is 20. Ward B one is for 80 world. And now if we can simply compare the currents at this Norby, you see, four amperes is ending the north from the left and 20 impairs is entering the north from the right. So that is a total off 24 impairs ending the north and downwards. You see, 24 amperes is leaving. So definitely guess yell is working here. And similarly, if you apply Kerviel on this first loop, you see, there is ah world his eyes off 500 wars and that is balanced by do world is drops the first word to drop off 20 words and the second voltage drop off 4 80 volts. So from these values, we know that all our results are correct and these are working. So that is how we can solve simple circuits containing dependent sources just by harnessing the power off owns Law and Kiss, Yell and KBL. I hope this was helpful. So in the next lesson, we're going to do yet another example containing dependent sources. So ST Joan and see you in the next lesson. 41. 228 EXAMPLE 2 of Circuits Containing Dependent Sources: Hi and welcome back. Here is another example containing a circuit with dependent sources and were asked to find the value for we not in the circuit. So we're given the polarity off wiener and narrative voltage across this last resistance and that is barred one and in second part were asked toe just a result off part one by verifying depart conservation in the circuit. So this is again quite similar to the previous example. But the configuration off this circuit is quite interesting. So first of all, let's do some visual inspection and then we will solve the problem. Now, here you can see there are two loops, one on the left and the other one on the right. And both loops are connected together through one wire. So basically, this means that there would be no current flowing through this middle wire because current needs apart to go and a path to return through. Okay, so if the current goes in this direction towards right, then it would have no path toe come back. So this middle wire, it won't have any current. So basically, there would be current flowing in this loop, and then there would be another current throwing in this group. So let's do a little bit off labeling. So this is the current I s which is given to us in the question. And basically, whatever this current is, we multiplied with three to get the voltage off this dependent voltage horse. So basically, this, uh, this world, this source is a current dependent world source. If this is win or bridges, the worlds across three owns resistance. With respect to that, let's also right. The current, which is I not so since dorms and three homes are in Siris, the same current would be flowing toe dorms and three homes. And we call this I not? No. In part one, we need to find our developed for we not. But look at this. If we simply know the value for I Nord, we can multiply it with three homes because these urgencies and that will give us the valley for we know. So if we simply no developed for I s and I Nord, we would be able to calculate devoted for this hold the source. And ultimately we confined we not. However, just finding I s would not be enough because with that, we can only find devoted for this world a source. But we won't be able to find how much wordage is dropping in the storm's resistance. And as a result, we won't be able to find this we not so finding I s And I know art is basic in order to find all the unknown variables. Because ultimately we know we have to verify the power conservation. So we need all the unknown voltages and unknown currents as well. So let's go with the first part and let's try to find our develops for I s and I Nord. And for that basically, we would need do independent questions. So if we apply Kerviel on this loop as well as on this loop, we would have to independent questions and so that we can find the values for I s and I know and ah, we would Jews Aziz usual go with the clockwise direction. So in clockwise direction, this 10 words would be a voltage rice and then says, Since this I s would be going down through this 600 assistance. This would be a voltage drop. Okay. Similarly, for the second loop, the current minorities lets his humor is going towards the right. So through the storms resistance, the world days would be dropping in this clockwise direction. Okay, so let's look at the first look. The total width is rises 10 world and the total voltage drop is the voltage across six on resistance. So let's write it down. Then where did rise is equal? Do will teach drop across tricks on resistance which is six times I s six, I guess. And you can see right away from this question we can find the value for I s, which turns out to be den over six, which is one point 67 in peer. If you do the calculation. So right off the bat we were able to find one off the unknowns. And now if you have, like Ariel in the second loop, then the total voltage rise would be three I s and the total loyalty drop would be the drop across dorms and the drop across three homes. So three I s, which combined is actually a vaulted that is equal to the water drop across this presents since is do I not true? I north plus three times the same current I not because these Aaron Series three i north and that is equal to do. Plus three is five I north And from this we can dried I know equals do 3/5 I this not since I s has already been calculated. So we will put in the values here 3/5 I s is 1.67 So if you multiply them, you would conclude that I Nord equals toe one in peer. So that is our second Vidia ble. You're just formed out and now toe simplify the remaining solution. We can mention all these colors on the diagram So I s is 1.67 appears 1.67 in piers going toe the ride this I know it is equal to one appear and accordingly we not weaken Find out directly using homes law we not is equal to three OEMs times one ampere So three times one This implies we not equals two three world So that is the solution for first part which we can right here, three board So the first part has been taken. Care off now we need to look at the power conservation and we need to verify that the total parts and Richard is equal to total power. Disip Richard So let's say this was the part one. And now let's continue toe part two and let's make a separation between decide and the other side. Now, you see, there are three resistances in the circuit and there is definitely no question, no confusion that all these resistances are going to dissipate power. Now you see 1.67 amperes is going upwards in this world resource and that current is actually going from negative to positive terminal. And when you see the current flows from negative to positive terminal, it is a case off power generation. All right. Similarly, this one appears is flowing upwards through this dependent world resource and as a result, it is going from negative to positive terminal which is again a case off power generation. So you see, both these vaulted sources are generating power and all the resistance is are dissipating power. So now we can find the power for each element and then we can find their total. So let's start with the power for 10 words. Source and that is equal to re I were worked age voltages 10 ward times The current is 1.67 1.67 and that turns out to be 16.7 Ward. And since this is a case off power generation, we have to attach it attached with it a negative sign, which means Asper passive sign convention. That has to be a negative power. Then for this voltage source three I s the power for that is going to be three power for three. I s is again going to be equal to the rally for the water source, which is three I s times the current flowing through that which is one ampere. So one. So basically we simply need to multiply three with I s So that is three times 1.67 and that is equal to five ward and again with a negative sign, because this is again a kiss off power generation. So the daughter power generator is equal to the sum off minus 16.7 in minus five, which is equal to minus 21.5. What? So that is the total amount off power generated. And now let's look at the power dissipated by each of thes Resistance is the power for six homes equals two. And for resistance is we will use the formula I scare are so I is 1.671 point 67 scared times six. And if you do the math, I think it turns out to be 16.7. What? Oh, and by the way, I found a mistake here. When you add minus 16.7 and minus five, it turns out to be minus 21.7 Ward, not Manus. 21.5 words. So let me correct this year. So that is the first power dissipated by the 600 resistance than the power for storms. Resistance is again using the same formula. I scared are where I is. One appear one scared times, two homes. And that is equal to To what? And both off these powers are going to be positive because these are power dissipation. Last word, nor the least we have. The three owns resistance, and the power is the current scared times, the resistance itself. And that turns out to be plus three. What? So if we add all these powers dissipated than power Dissipation turns out to be 16.7 plus to bless three. And that turns out to be 21.7. What So if you compare power dissipation, which is 21.7 and power generation, that is also to anyone foreign seven with the opposite side. So that verifies that the total power generator is equal to the total participated. And there is also proof that whatever calculation videoed from part one, that is correct because it led us toe the power conservation being satisfied on the circuit . So I hope that was helpful. And now you understand how to solve simple circuits with dependent sources. So thank you for watching, and I will see you in the next lesson. 42. 302 Resistors in Series: hello and welcome back in the previous section, we studied that whenever two elements are connected in series, they only share a simple nor in between. So here, in this particular case, these two elements we don't exactly know what these elements are these air just shown with these boxes. But from their connection, we can see that they're connected in series and in the case, off series connected elements they all share the same current. Now here is an example off a series connected resistance is and you can see R one and R do are shooting a simple Nord. Similarly, are doing are three are sharing this simple North rt and our for our shooting this simple North. So we can say that r one r two r three and r for these are all connected in Siris Now a lot of times in circuit analysis, we have to simplify circuits. So in this particular lesson, we're looking at a way to simplify. The resistance is connected in series, so we're basically looking at a way toe. Simplify all these four resistance is and replace them with a single resistance R e Q so that this beer's exactly the way these four cities connected distances are. So I have drawn these two points x and y so on the left off this ex and why we have this world resource and similarly in this diagram. So the left hand side of both circuit is the same. But on the right hand side here we have thes four resistance is and here we are replacing them with just a single resistance card, the equal in resistance. So it turns out that whenever we have multiple resistance is connected in Siris they're equal and resistance is equal to the sum off. All the resistance is connected in series So R one plus r do plus r r three all the way up to our end here. In this particular case, we have only four resistance is so R S O N is equal to four. So we will be only adding thes were resistance is But this is general formula and this applies toe any number off resistance is we're en ranges from two all the way up to infinity. So there is the general formula. But we should also look at how we arrive to this conclusion. So let's look into this formula and let's try to derive word. So here we have the same circuit drawn again with X and wipe wires were on the left hand side. We have this Walter source and on the right hand side, we have these four resistance is and here we have it's equal and resistance replaced for all these four resistance is now looking at this circuit. You see, there are five elements of wilted sores and for resistance is and we know that all the four resistance is are going toe always dissipate power resistance is can never generate power. So the only element that is going to generate power is going to be this voted source and from passive sign convention. We know that the elements which generate energy, they produce current in the direction off negative to positive terminal, so accordingly, the direction for the current has called this I s This is the current supplied by the world , his horse. So it is going to be in the direction off negative to positive polarity. And since there's only one part for the current to flow so accordingly, this current has to flow in this direction. So according Toa This name convention, this is our one. Let's call this one and here it is going to be in this direction. Let's call it I to let's call this I three and let's call this I for so you can see where this direction is going. It is going floor. The current is flowing in the clockwise direction and once we know the direction off these currents, since we know that these resistances are dissipating power So in the case, off dissipation current floors from positive to negative so accordingly this has to be the positive terminal This the negative terminal and this is our one. So let's call this world age V one. We can call this world is we do this as we pre and ah this world which has discolored we for now. First off all you see that all these currents are going to be exactly the same. Why? Because all these elements are in Siris. So if you look at this nor the entry guarantees I s the living current is I want So I s has to be seen as I want similarly at this north the engine got it is I won I do Is the living current support off them Have to be the same as per case Yell so according toa que ciel, we can say that I s equals two. I've won because toe I two equals toe I three equals toe I for and now let's apply giv e l in the clockwise direction. So if he apply KBL you see in the clockwise direction there is only one voltage rise which is we s and the all others are worthless drops we want we do with re entry for all of them are voltage drops So let's write worked age rise on one side we s and there is equal to the sum off the voltage drops as Burke Aviall So the summer voltage rises is equal to the sum of voltage drops which is we won plus we two plus we three plus we four we can make use off owns law toe right These voltages in terms off currents and resistance is now we know that all these currents are equal toe I s so if we write this, we won in terms off the current and resistance begin writers as i one r one But I want is equal to i s So we can itis as I s r one Then we do can be written as I do are do But I do it same as I s So let's write all of the's in terms off i s So if we write I s r two then VT would be I s r three and before would be I s r four No, we can take I s common So the s is equal to I s taken common and r one plus r two Bless our three Bless are full now since we are replacing all these four resistance is with an equal and resistance We know that both these circles are going to be equal So what if we apply our owns law on this circuit? We know that we have the same current eyes flowing because the left hand side Zehr same in both circuits. So if we apply whether we apply homes law, Soviet physical toe I SRE Q Or even if we apply Kerviel So let's apply give you we s that is devoted tries and this is going to be Walters drops. Let's call it. We and that musical to I s Which is the current flowing here I s R E Q. Since these equations have the same left inside the horizon, size must be the same. So if we write this thing as equal to this ah, I s r one plus r do Plus are three plus r four because toe I s R E Q So from this we can write that R E Q is equal to our one plus our to bless our three plus r four. So this equation implies that when we have these four, resistance is connected in series that some off these four resistance is is equal to R E Q . So we can replace all these cities. Connected resistance is with just a single resistance, R e que, where argue is equal to the sum off doors series connected resistance is so that is the formula for this particular scenario. And in general, the formula for argue for Syria's connected resistances goes like this are accused ical to r one plus r do plus are three plus all the way up to our in where this applies for any number off resistance is and this thing can be written in a mathematical form like this Sigma off our I where I ranges from one all the way up to in. So there is the formula we can use to simply fire. Resistance is connected in Siris. Now, one important observation from this formula is that the equal in resistance is always going to be greater than the largest resistance in the cities connection. Basically, this has to be larger than the largest resistance in this. And it makes sense because the argue is the some of these resistances. So the sum is definitely going to be greater than the biggest value in this expression. So there is how we can simply fire resistance is connected in Sousse. Thank you for watching and see you in the next lesson. 43. 303 Resistors in Parallel: hello and welcome Back in the previous section, we learned that two or more elements are said to be connected in parallel. If they share the same pair off north like these two elements here, you can see that their upper north and lower north both are shared by thes two elements. So we would call them connected in parallel. And the property of the par little connection is that all the elements connected in parallel share the same voltage as you can see in this case. Now, when we say parallel connection, there is a word off caution. Do not make the mistake off thinking that two elements are in parable if they're drawn in parallel in a diagram, because that's not what we look for. The only requirement for parallel connection is that the elements have to share the same beer off yours, and that's it. So, in other words, two elements which might be drawn in parallel their connection might not be parallel and vice worser. And to illustrate that point here we have this diagram where you can see that R one and r three. Apparently these are both vertical, so one might say that they are in parallel, but that is not true because for connection we only look at the North. So here they're lower north is common. But the upper north between R and R one and r three thes north are different because they're separated. Toe are too. So they're not sharing the same pair off north. That's why are one and Artie we say that they are nor in Barlow Connection. Similarly, Look at this setting here R one and r two. Even though they want is vertical, the other is horizontal, so they don't look like drawn in Parral. But as far as the connections are concerned there, this nor does seem and the other north is also shared by these two. Resistance is so yes, R one and R do are connected in parallel Now, just like we learned in the previous lesson about how to simply fire resistors connected in Siris. Here we are going to learn how to simply fire resistors connected in parallel. So to illustrate that here we have this drawing where you know we have two points x and y On one side we have this voltage source and on the other side, we have these four resistance is and all of them are connected in parallel. You can see that all these four resistance is were are one artwork in our for they're sharing the same beer off north. So yes, these are in parallel and we're looking for a way to simplify this so that we can replace this right inside off. These four resistance is with just a single equal int resistance. So they're left inside is exactly the same. But on the right hand side, we replace this wall resistive network with just a simple resistance. So we're interested in finding out that for a given number off resistance is with specified values. How can we find their equal in resistance? So it turns out that we can find this equal in resistance using this formula and as part this formula, the inverse or the reciprocal off the equal in resistance is equal to the rest of broken off the first resistance, plus reciprocal off the second placed reciprocal off the third and so on and so forth. So here we have just four resistance is so we would have the recipe locals off. All those four resistance is added together and that would be cool toe the reciprocal off equal and resistance. So there is our weaken. Simply fire resistance is in parallel. But more importantly, we need to understand how we guard toe this conclusion or to this formula. So let's try toe derive that formula. So here we have the same second drawn again and we want to replace the right hand side with something simpler. So let's label this diagram a little bit. First off, all you see that there is only one active element which is generating energy. All others are resistance is which are going toe disappeared energy. So since this is going to generate energy, its current has to flow from negative to positive Terminal Asper Passive sign convention. So let's call this current I s And now this current would go words right? And then it will go down through all these resistance is so let's call this current flowing through our one as ah I one toe are toe the current lease Collard. I do this called this current I three and this Garant I for now. By applying KCIA on this north, you can see that the entering current is I s and the leaving currents are I won through I for so Asper Casey. L begin, right. I s because to I one plus I do bless I three plus i for And now you see that all these resistance is are in parallel with the voltage source. So this world, it would be faced by all thes resistance is so I want it would be cool to reassess over our one. Similarly I do would be we s over our do I feel would be equal to V s over our three and so on. So let's right these in terms off world age and resistance. So I one would BVs or are one bless the s or R two Plus we s over our three plus we s or are four and article toe I s Now you see, we have devious term the beating in all these fractions so we can take this common and we can iterate as we s times one over r one plus one over r two plus one hour are three plus one over r four. Now if we apply a similar kind off labeling on this diagram here, the only difference is we have just one resistance. But the current would be same. Its direction would be seem since both circuits are equal int. So I Yes, If we write the equation for this, I s that would be called to the vault is or the resistance. There is only one resistance. So this equation would be simpler. I s would be called to BS or R E Q or you can write Weah's separate. So that would be one over R E Q. Now, if we compared this equation with this equation, you can see that there left hand side is same. Both have I s and I s. So accordingly, the right hand side should also be seemed so here. This term should be equal to this. And we have es in both these terms so we can ignore es And that means this whole thing inside the bracket should be called. Tow this thing in the bracket and from that we can ride one over r e q equals to one over r one plus one over r two plus one over are three plus one over r four. So as but this equation, we can replace all these four resistance is with an equal int resistance. And ah, the value for this equal int resistance can be found out using this formula where the reciprocal off this equal in resistance is equal toe. That's some off receive brokers off all these resistances in parallel. So that is the proof off the formula we saw from the previous slight. Now, this formula applies to when we have four resistance is in parallel. But for a general case, where we have end resistance is the formula is this the reciprocal off equally resistance equals to the reciprocal of first press reciprocal offs. Again plus third place on our Ndele does he broke ALOF and resistance and that can be written mathematically in the submission form where we have Sigma off one over r I where I start from one all the way to end. So using this formula, we can calculate the equal in resistance for any number off resistance is connected in parallel and with any resistance values. Now, one thing you need to keep in mind is that, unlike the case off, serious resistance is where equal existence was greater than the largest resistance in the Cities Network here we're talking about in terms off these reciprocal, so everything is upside down and accordingly, that statement also reverses. So in case off parallel resistance is it is totally opposite. Here we have equal resistance is always smaller than the smallest resistance in the parallel connection, and there are a few more things that you need to keep in mind as far as parallel resistances are concerned. The first thing is that since this barrel formula is in terms off the reciprocal and we know that the reciprocal off resistance is conducted, its so it might be a bit easier if we use conductors instead. Off the resistance is so, for example, here that is the formula. So we know that the inverse off the resistance is conduct mints. So this one over r E Q. We can write us as g e que are equal and conducted its and that is equal to the reciprocal off. First resistance would be equal toe the first conduct INTs Similarly, the second conductors and so on and so forth. So that way, by converting these resistances into conduct, Ince's we can get it off these reciprocal terms and the other important thing you need to keep in mind is that when we have only two resistance is connected in parallel, then we can simplify this formula a little bit. And ah, to show that let's assume that we have to. Resistance is connected in parallel, which are R one and R two and now we can take the L C M and ah, we get R one R two as L. C. M. And in the new military we have R one plus R two. And since we are interested in finding the equally resistance, we flip both these fractions. So we get equally resistance equals two our when our do over r one plus r two. So this formula shows that when we have two parallel resistance is there equal resistance is equal to the product off. Those two resistance is divided by the sum off. Those two resistance is, however, do keep in mind that this simplification off the formula worlds only when we have two parallel resistance is right. So we have to bury resistance is orm or we would have to refer to this original formula. So the simpler form it only works when we have two parallel resistance is so that was all about popular resistance is and how to simplify them to find an equal and resistance. In the next lesson, we apply the series and parallel simplification rules that we just learned in an example, so see them. 44. 304 EXAMPLE of Series and Parallel Resistors: Hello and welcome back In the previous lessons, we have learned how to deal with resistance is in series and parallel. And now it is time toe. Use that knowledge to solve this circuit. So here we are given this circuit and were asked to find the values for I s I one and I do in the specified directions. So I s has pointed upwards. I want tonight to our pointed downwards and we're going to find their values now. First off, all you should remember that the voltage source has a specific value for world days, but its current is not specified. The reason is that the amount of current supplied by a voltage source really depends on how much resistance is connected to that pulled its source. So the same world it soars can provide a large current. If the resistance connected to it is small and the same world it soars would provide a very small current. If the attached resistance is very large, so it is involved off homos. Resistance is connected to that. So since we are asked to find I s we really need to find our daughter resistance that is subjected to this world a source Only then we will be able to find I s so for that reason, we will have to simplify. All these resistance is to find the total resistance this world, the source is saying and to simplify any resistive network, you need to look it. Any resistance is that are either in Siris are in parallel. So if you look at this right now, we can't see any barrel combination. Off resistance is the only combination vegan see is a sees combination off three and six homes. So that would be the first step. And that is where we start. And from the lecture on series, resistance is we know that they're equal and resistance is the sum off all the series Resistance is so here three and six there some would be nine. So if we call, they're equal and resistance r e Q one. That would be cool to six plus ah, six plus three and that is equal to nine homes. So basically we can replace these two. Resistance is with a single nine home resistance. So if you do that, our circuit simplifies toe this circuit and now you can see that there is no city is combination anymore, But now we start seeing a parallel combination off 18 and nine. So basically this simplification goes step by step here. Whatever combination we're going to see, it won't be available in the next step. But here now we might be able to see a totally new combination, like in this case, this dinner nine. Now it is in Parliament so we can find their equal in resistance. And let's call this our cue to no from the parallel resistance is formula. You might remember that if we have only two resistance is the reciprocal formula. Simplifies toe R E Q is equal to the product. Off to resistance is divided by their some, so that formula would be are one times are two divided by R one plus R two. So if we put the values are one is 18 and are do is nine or we can assume their assumed them otherwise, but it would still be the same. So 18 times nine divided by 18 plus nine. So ari que toe turns out to be 18 times nine as 1 62 an 18 plus nine as 27 so if you do the math, the R E Q two turns out to be 1 60 Door 27 is six comes, So now we can replace these two barrel resistance is with a single six homes resistance. And if you can do that, our circuits simplifies this simpler circuit where we have four armed resistance as pre as as before. But 18 and nine have been replaced with six armed resistance, and now you can see that it is much easier for us to see the total resistance since there is only two resistance is and put off them are in cities. So for and six homes, they're equally resistance is four plus six, which is 10 homes. Now let's label this x and Y on all diagrams. So that began easily track the simplification off circuit. So this was X. This is why this is X. This is why likewise we can also label I s So this source current is I s This is I s Then we have I won flowing through 80 norms. So this is I one and I do is throwing through three and six. So they're equal and his nine. So this that resistance would have the same current because they're in Siris. So let's call this I now we can go ahead and find I s because here you can see we have the daughter resistance, which is then, homes. So I s is equal to weaken you zones law year. So I is equal to be over. Our Asper owns law, So the voltage is 1 20 world and the resistance connected to that is the total resistance which is four plus six groups. So I s is equal to ves over our where V s is 1 20 ward and our is four plus six Article 10 homes. So this implies I s because 21 20/10 and that is equal to 12 in peer. So Dad is our first result. And let's level it here. Well, beer and well, I'm here. What if we have the world is between the bars x and y. If we have that boulders we can easily find I won by applying homes law on this resistance and similarly we confined. I do by blank homes law on this series combination off resistance is so to find this world is between X and Y Remember this x y they sex a y and this x y they're all equal int So if we find the voltage here, that would be the world days across all these diagrams. So let's find that world is you see the resistance, this resistance would have the same current which is coming from this source because there is only one part for the current. So if this current is 12 impairs going upward, this current would be also 12 appear going downwards and from the knowledge off resistance , we know that the disappeared power and because of that reason, the current always flows from positive terminal toe the negative terminal. So now we can apply owns law to find this world it So let's call this wee one positive at the top negative at the bottom and that would be same here, positive and negative. Let's call this we won and also here not to find this we won begin simply apply homes law on this resistance so we want equals toe The current flowing through this resistance which is 12 appear times the resistance itself, which is six homes. So we want turns out to be 12 times six, which is 72 fort. So we can label this here we one equals 2 70 toe world and also here as well 70 towards No , it becomes really easy to find I want and I do. And that is simply a matter off applying on floor on this resistance and this resistance. So I want let's use this diagram because this is simpler, less messy. So I want is equal to the voltage across this resistance which is 70 towards divided by the resistance itself, which is 18. So I want equals toe 72 word divided by 18 homes. And this implies I one equals two 70 do over 18 is equal to for beer. So that is our second result. And lastly we confined. I do by applying owns law on this resistance. And remember, thes two resistance is are in parallel, so this resistance would also have this same voted 72 wars. So I do equal toe V, which is the voltage across this resistance, and that is 72 world divided by the resistance itself, which is nine homes. And this implies I do equals toe 72/9 turns out to be it in peer. So with that, we have found all the values for the unknowns that were asked in this question. So you can see that we have used the rules for series and parallel resistance is in conjunction with the owns Law and Kickoffs Law to find all the unknown variables in this question. Now we can go one step further to verify if our answers are correct and we can again make use off the kickoff laws and the maybe Gourcuff's current law because voltage law toe very fire our answers. So first, let's apply gcl and see if it works on and in given north. So if you look at North X, you see the entering current is I s and there are two living parents I want and I toe so I s should be equal to the sum off the two living currents. I one and I two and, uh so I s should be called to I one plus I to And if you put in the values, what is I s that is 12 in peer and that should be going toe I want which is foreign Pierre plus I do, Which is it in peer? So this implies that uh, 12 ampere is equal to four impair plus eight appears that is equal to 12. So since left inside and writer insides are same. So definitely case yell works for these values. So there is a proof that our values are correct. We can further go ahead and apply it on the north y again. We have the same values, so that is going toe work. You can also tow this ratification with the help off Gabriel by applying the Kickoffs voltage law on any loop. So let's applied on this loop here, you can see there is one voltage source that has one worlders and the other two mortgages are across thes resistance is so if we apply Kerviel on this loop and let's apply this in the clockwise direction you see that in the clockwise direction this is a world is your eyes and the remaining would be wordage drops. Because remember this current it is going through this resistance in this direction so accordingly this would be Plus, this would be negative and likewise this I won with a positive value. It is going downwards so the upper terminal has to be positive. The lower terminal has to be negative. So the voltage rise in this loop should be equal to the total voltage drop in this loop. And since this nine arms and 18 arms resistance is are in parallel, they have the same voltage across these resistances. So it doesn't matter whether we apply KBL in this loop are in this bigger loop. Both those questions would be same. So if he applied in this smaller loop, the portal voters rise as 1 20 board and that is equal to the sum off worlders drops. So the first word is drop is across this forearms resistance and we don't know its value directly. But we can write it in terms off homes, law musical toe ir So the world is across this resistance would be the product off the current through this resistance times the resistance value. So this current is going to be same as I s because they're in Siris So I yes, we know it is 12 appears so this world is would be 12 time the resistance, which is four So their product is the first Walters drop and The second voltage drop is across this 80 norms resistance and that is actually be one. And we have already found we want to be 72 wards. So if we simplify this, it turns out to be 1 20 on the left hand side and that is equal to so this 12 times for the physical to 48. And when we had 48 to 72 this turns out to be 1 24th So gay VL it also turns out to be working for these values we have found out. So this is another proof that our values are correct and we can go even one step further by applying the law off conservation off power on the circuit. So, as per the law of conservation off power, the total power generated in the circuit must be equal to the total power dissipated in the second. So the only power generator is going to be the power from this water source and all the powers for these resistances are going to be The power's dissipated. So the power by this world is wars must be equal to the power's dissipated by all these four. Resistance is added together, so that should also work out. But I am not going to do that. I would leave it for you to do so. Overall, we have learned in this lesson how to use series and parallel resistance combinations toe solve a circuit and find the unknown variables. So I hope you found this useful. Thank you for watching and see you in the next lesson. 45. 305 Voltage Divider Circuit: hello and welcome back in some situations, especially in modern electron ICS and integrated circuits, it is required to develop multiple Walters levels from a single world. Did supply, for example, A said it may be connected to, ah, five words hold its source. But somewhere in that circuit, we may also need some other world is like 1.8 words and this can be achieved using something God, a voltage divider circuit. So here we have an example off awardee divider circuit. So we have vaulted source and that is connected Toe to resistance is R one and R two. So we know that as these resistances are connected to the voltage source, it is going to supply some current I. And as a result, when this current flows through these whole loop two voltages are going toe appear across thes two. Resistance is depending on the values off R one and R two. So the voltage across our one we call it we one and the world is across our do we call it. We do so in order to understand the working off this world to do our circuit, let's analyze it and find the bodies off we won and we to. So first of all, we know that there is only one part for this current. So this current goes up and then goes to the right and then it will come down. And in this way it will be flowing in this clockwise direction. And when this current goes downwards, we know that for resistance is current always goes from positive to negative terminal. So that is how we can say that the upper terminal for both resistance is going to be positive and the lower terminals are going to be negative. Now we know that the same current is going to flow. So this is the same current I. And if we apply Kerviel on this closed loop, let's say in the clockwise direction than from give yell. We can write that the sum of wordage rises in this loop is equal to the sum of four days drops. So in clockwise direction there is only one voltage rise, which is we s So that goes on one side and there is equal to the sum off voltage drops which are in this case we want and we to We won. Plus, we to And we can drive thes voltages in terms off homes law. So v one is equal. Do I are one? I are one plus we do is equal to I r two. I are due and that is equal to B s. So from this, we can take I common to the physical toe R one plus r to And from this we can write that the current flowing in this circuit is he could do the source world did do ordered by r one plus r So that is the first result. And now we can ride the we won and we do individually So using warms law, we can write We won as just like here we can write it as I are one there I are one So we know the value for I we can write it as we s we s who were r one plus r two and we can write it in a slightly different form. Ah, we can ride. We one equals two If we separate out, we s from all these resistance is we can write it as well. Yes, time are one over are one bless our do so Let's call this question one, and likewise we can write an equation for we do and that is equal to i r two. So if we write it as our do and for I weaken, substitute this value b s or r one plus r do So this implies we do equals toe again. We will separate out we s and right All the resistance is in the bracket So that is you're left with are too Do I did Why are one plus our toe So we call this equation toe So these equations one And to show that re one and we do our the fractions off the supply Voltage v s in each of these fractions is the ratio off the resistance across with the divided voltages defined toe the some off the two resistance is, for instance, this veto is a fraction off. We s where they're fraction is the resistance across which we do is specified, which is our do divided by the sum off the two resistance is now, since this ratio is always going to be less than one, the divided voltages we won and we do our also always going to be less than the source world age. We s now in many applications. We desire a particular value off we do. While the supply Walters is specified for that purpose, an infinite number of combinations off R one and R do can yield the required ratio. For example, if the supply voltage is 15 wars and we do is going to be five world, that means we need a ratio off we do over V s is equal to 5/15 which turns out to be one Kurd. So this ratio is satisfied whenever we have. Our do is equal to half off our one so you can try this out. You can fill in any values for R one and R two as long as our musical to half are one. You will figure out that if the supply work is is 15 wars than we do would turn out to be five world. So this shows that there are countless choices for R one and R do in order to get the desired voltage. But here we need to keep in mind that not all resistor choices are good choices. There are some factors we need to keep in mind while choosing the values for R one and R two in order to get her desired voltage ratio. And the 1st 1 is the power losses that occur by dividing the source voltage. Because you see, at our do, we are extracting some useful voters. But there is going to be some power losses in our one, so we need to keep that in mind. And the second factor is the effects off connecting devoted divider circuit. So some other circuit companies, because those companies will draw some current and hence some power as well. So these are the factors we need to keep in mind while making a good choice for R one and R two. But overall, now you know that how to find out the we won and we do values when you are given a voltage divider circuit. So I hope you found this useful. Thank you for watching and see you in the next lesson. 46. 306 Effect of Load and Tolerance in Voltage Dividers: Hi and welcome back In the previous lesson, we said that the voltage we want at our toe is needed to be supplied to some circuit or a circuit component called Lord. So here we have connected a resistor R l in parallel with R two and this resistor r l is acting as a lord on the voltage divider circuit. A Lord on any circuit consists off one or more circuit elements that draw current and hence power from the circuit. So this world is across our tow, which we were initially calling v do. Now, let's call it we or we out port because now we're using it to feed some Lord which is an external circuit or a circuit competent. So since this R l is in parallel with our do so, accordingly, the equation for the world divider would also change. So the new aggression is this We out is equal to ves times argue over r one plus r toe. So if we compare it with the original will to do it every question here instead of our do we have replaced it with our e que where argue is actually the parallel combination off r two and R L So, more specifically argue is equal. Do the product off. These two parallel resistance is divided by their some. Now, if we take this value off R e Q And if he substituted in this new miniter as well as in this denominator, this is what we get. We are is equal to V s times this thing, which which was actually argue. But its value has bean substituted, divided by r one plus the value off are equal and substituted. And if he simply fight further began righted as we out is equal to V s times our do over r one plus arto where are one is being multiplied by this factor in this bracket? Not this complicated fraction can be simplified in many ways, of course, but we deliberately simply fight it in such a form, which is compared able to the original Walter to other equation. The only difference is this are one is being multiplied by this factor, Okay, one plus our do over r l. That is the only difference. Otherwise, this equation is exactly same as the original Walter Strider question No. In this aggression, if the Lord resistance is very, very large. What happens is that this equation becomes comparable to the original voltage divider. Question. The reason is, if the Lord resistance is infinity, then that denominator in destruction is infinity. And whenever the denominator is infinity in a fraction, irrespective of what the new miniter is, the fraction reduces to zero. So when this becomes 01 plus zero is one. So everything in this practice is equal to one. So that means, whether we write it or not, it does not make any difference. In effect, this equation becomes exactly this. We out physical TVs as it is then our do over r one plus R two. So if he applied this condition, then this equation reduces toe the original. What divider in question? Likewise, if the Lord resistance is very, very large compared to our do or this is another way off saying that distraction becomes negligible. Then again, this would become very close to zero. So one plus zero is still one. And again we can say that this fraction would be seem as this, and as a result, the relation or the ratio v out over V s, it would be undisturbed, whether we add that lord or not. So overall, we can summarize that if any off these two conditions satisfy, then connecting that Lord does not make any difference to the working off that Walter's divider. Another thing about voltage divider circles that we need to keep in mind is that these are very sensitive to the dollars is off, the resistance is, and dollars means arrange off possible values. For example, whenever you buy a resistor, its value is specified as blessed minus one person or plus minus 5%. And so on. Resistance is off. Commercially available resistors always very within some percentage off their stated values . No, let's look at an example off the effect off resistor dollar and says in a voltage divider circuit. So see you in the next lesson. 47. 307 EXAMPLE of Resistance Tolerances in Voltage Dividers: Hello and welcome back in this lesson, you're going to look at the effect off tolerances in the resistance is on the performance off a voltage divider. So here we are, given this circuit where this world it is mentioned as we north. So we're toward that The Torrance's off. Both these resistance is our plus minus 10. Person, they say, is that the actual values off these resistance is lie within plus minus 10 person off thes stated values. And actually, this is quite a big variation or quite a big tolerance. So we're asked to find the maximum and minimum values off this output voltage. So if you remember the lesson on voltage dividers, the diagram we saw in that lesson in that diagram the upper resistance we would call it are one in the lower resistance. We would call it are too so accordingly. This whole days, we were refering to that as we do. But here in this scenario, we are calling it we north or basically this is the output world, as we're trying to get from this world is divider. So the formula for the voltage divider waas If he applied in this particular scenario they are put worlders is equal Do the sport supplied Walters We s times the resistance across which we are measuring this output voltage So that would be our do Divided by the sum off to resistance is in the world is divider So that would be our one plus r toe So that was the generic formula from world dividers lesson. Now, if you put in the values we get, we out equals toe Bs is 100 words in this case. So let's write it as 100 now our to it is 100 key. Okay, so 100 key divided by R one is 25 G plus 100 games So normally we would simplify these numbers and that would give us the exact output voltage. But here we are given some tolerance for these resistances and as a result we're going to get a range off the artwork values. So toe fined the maximum value for this output world is you see that we out Max the out Mex that is equal toe this 100 words. It is going to stay the same. There is no fluctuation in this world. It's source that is going to be fixed. The only fluctuation we will see is in the valleys off. These resistance is so whenever this fraction is maximum, that is when we will get the maximum value for our port. So when are we going to get the maximum value for this fraction? Well, when the new militaries maximum and the denominator is minimum, that is when the fraction value maximizes to maximize the value off this numerator we have toe. Look at this. Baldwin's. So when we have this plus 10% dollars in this numerator artis first are this low resistance . That is when our new military is going toe maximize. So if we add 10 person fluctuation toe this resistance, it becomes one then. And by the way, all these resistance is in numerator and denominator are in Kellems. So there's no need to write this gay sign everywhere. We can just skip that that once we have chosen a particular value for this tolerance for a resistance, we have to stick with that. So once we jaws plus 10 person, we see that this are do is repeating in the denominator as well. So here we have written 1 10 gay. So we will need right the same value in their denominator as well. Now we need to minimize the value for this denominator and that would be minimum. When we have the minimum value forth, this are one and that would occur when the tolerance is minus 10%. So when we apply minus 10% dollars on this 25 k resistor, it reduces toe 22.5 game. So with these values, the value for this fraction would be maximum and that would correspond to a maximum value for the airport. Now, if you simplify that, it turns out to be 100 times 1 10 Derided by Granny DuPont five plus one den is 1 32.5 and that is equal to 83.0 toe board issued with the calculation. Likewise, to find the minimum value for this output world age Ah, the 100 word would still be the same. But now we have to minimize the overall value for this fraction and that would be minimum when the new military would be minimum and the denominator is maximum. So the minimum value for the new military would be when this resistance has minus 10% dollars. Accordingly, the minimum value for this resistance is 90 k Okay. And ah, since this resistance is repeating in the denominator as well, we have to also write the same value in the denominator. And to maximize the value for this denominator we have produced the maximum value for this are one. So when we apply plus 10% dollars on this resistance, it turns out to be 27.5 key. And now we can simplify these numbers so 100 times 90 over 27.5 plus 90. It is equal do 1 17.5 and that is equal to 76.6 volt. So, overall, you can see that the output ranges between a minimum value off 76.6 world and a maximum value off 83.0 to 4. So that is the range, and that is actually quite a big range. And that is a direct draw back off. Choosing resistance is with a high tolerance value, so you can see that when thes resistance is have high trawlers, which means their values are not very accurate. That translates into our non decorate Walters divider and if he wanted an accurate are put boulders. We have to make sure that the resistance is used are decorate as well. So I hope you found this useful. And now you understand the effect off Lawrence's off. These resistance is on the performance off voltage divider. Thank you for watching, and I will see you in another lesson.