Fundamentals of Electricity and Electronics | Leon Petrou | Skillshare

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Fundamentals of Electricity and Electronics

teacher avatar Leon Petrou, Engineer

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Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

Lessons in This Class

41 Lessons (3h 52m)
    • 1. Introduction

    • 2. Basic Concepts of Electricity and Electronics

    • 3. Power

    • 4. Kirchoffs Laws

    • 5. Types of Sources + Branches, Nodes and Loops

    • 6. Cramers Rule in a 3x3 Matrix +Example

    • 7. Passive Sign Convention + Example

    • 8. Series and Parallel Resistors

    • 9. Series and Parallel Resistors Example

    • 10. Current Division and Voltage Division + Example

    • 11. Wye Delta Transformation + Example

    • 12. Nodal Analysis + Example

    • 13. Supernodes + Example

    • 14. Nodal Analysis by Inspection + Example

    • 15. Mesh Analysis + Example

    • 16. Supermesh

    • 17. Supermesh + Example

    • 18. Mesh Analysis by Inspection + Example

    • 19. When to Use Nodal or Mesh Analysis

    • 20. Transistors

    • 21. Transistors Example

    • 22. Superposition + Example

    • 23. Source Transformation + Example

    • 24. Thevenins Theorem

    • 25. Thevenins Theorem Example (Part 1)

    • 26. Thevenins Theorem Example (Part 2)

    • 27. Nortons Theorem + Example

    • 28. Maximum Power Transfer + Example

    • 29. Operational Amplifiers

    • 30. Operational Amplifier Example

    • 31. Capacitors and Inductors

    • 32. Capacitor and Inductors Example

    • 33. Phasors + Example

    • 34. Phasor Arithmetic on Calculator + Example

    • 35. Complex Numbers on the Calculator + Examples

    • 36. Impedance and Admitance

    • 37. Impedance and Admitance Example

    • 38. Leading and Lagging Sinusoids + Example

    • 39. Sinusoidal Source Transformation Example

    • 40. Sinusoidal Thevenin Equivalent Example (Part 1)

    • 41. Sinusoidal Thevenin Equivalent Example (Part 2)

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About This Class

Electricity and electronics calculations made easy!


This course includes video and text explanations of everything in electricity and electronics, and it includes more than 40 worked through examples with easy-to-understand explanations. 'Fundamentals of Electricity and Electronics' is organized into eight sections:

  1. Basic concepts
  2. Basic laws
  3. Methods of analysis
  4. Circuit theorems
  5. Operational amplifiers
  6. Capacitors and inductors
  7. Sinusoids and phasors
  8. Sinusoidal steady-state analysis

These are the eight fundamental chapters in the study of electrical and electronic engineering.

Watch over my shoulder as I solve problems for every single electricity and electronics issue you’ll encounter in class. We start from the beginning... First I teach the theory. Then I do an example problem. I explain the problem, the steps I take and why I take them, and how to simplify the answer when you get it.

Meet Your Teacher

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Leon Petrou



Hello, I'm Leon. I graduated with a Bachelor's of Engineering degree with distinction from the University of Pretoria. I specialized in Industrial and Systems Engineering. I have a passion for problem solving and education. I love teaching others and simplifying the learning curve for engineering students around the world.

See full profile

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1. Introduction: welcome to electricity and electron ICS. My name is Yang, an industrial engineer, and I'll be your instructor for this course, along with my partner. Joining me on the Creates is off up engineering videos. The reason we created this course, it's because of the extremely high top operates for first year engineering students. Our vision is to increase the pulse rate for engineering Students around the world, in this course are pay attention to the small details and step us their processes to answering the questions. These details, by essential to build a good foundation and understanding off the concepts. And, like our slogan says, We don't lecture. We teach the major components off. This course include KBL and Casey, Energy and power nodal analysis and mission analysis, Dividends and Northeast Era as a lot of Sinus waits on faces. No, I'm going to ask you two questions. Are you stressed about getting the mark she wants? And second, he do you want to effectively cover the entire modules content in as short amount of time as possible. If your answer to these two questions is yes, then this is the course for you doing the requirements to taking this course on your no prerequisites. We only ask that you come with an open mind and ready to go view the course description. You know, if you want to see what this course entails, Andi, at the end of this course, not only will you be able to walk into that final exam with confidence, but you will be able to walk out with the mark she wants. 2. Basic Concepts of Electricity and Electronics: Hey, guys, in this video, be discussing the basic concepts off electricity and electron ICS on actually got some formulas and values that you need to memorize in order to do the calculations. All right, so, firstly, one what our is equal to 3600 jewels. This is useful power and energy calculations when you want to convert from the one form to the other, depending on what the question asks, The charge of an electron is equal to 1.6 times 10 to the 29 colon. Current is defined as the rate or flow off charge measured in amperes. That's the capital a not the lower case, either. The upper case, the formula to define charge is the derivative, so the formula defined current is the derivative of charge as a function of time. So that's equal to the changing charge divided by the change in time. So if this was illustrated on a graph over here, the current would be on the Y axis and time on the X axis and in the area underneath the function represents the value of the charge. Voltage is defined as the energy required to move one unit of charge between two points. So if we have two points like that between a resistance, the voltage is measured across this element. We has current flows through the elements right in the unit voltages V. That's once again a Capital V. Now this formula is very, very important. It's called Holmes Law. All right. On that is equal to the voltage that equals resistance multiplied by currents. I use this little triangle to remember the formula. So basically, V is equal to our multiplied by I r is equal to be divided by I. So it's just a little triangle that I like to use. And the unit for resistance is the Greek Omega I'm called owns. All right. Energy is defined as the capacity to do work. Measured in jewels like these are the two formulas you could use to calculate energy. The one is power multiplied by time powers measured in watts and time is measured in seconds and that will give you the energy and jewels. All right, is this formula as well? If power is given to you as a function of time like that, then you integrate it in terms of time between the two points in time. Andi, Certain definite integral on that will give you the energy. Power is defined as the rate at which work is done, measured in watts. All right on this, the falling equations you could use to calculate power powers equal to voltage times current. This is the most commonly used power formula. There's another triangles that you could you remember this formula worth? But there's also this formula here that you could use to calculate power. But it's not as commonly used in this module. They're more likely to ask this formula Alright, And just another thing you guys need to know is that if the power is absorbed, then the power is positive, and if it's supplied or delivered, then it is negative. In the next video, I'll be doing power calculations, just some basic examples. You know how to go about answering these questions 3. Power : in this video, we will be doing to power calculations. All right, we'll start with this one. Here. We had also is to calculate P one and P two p one is the power over here off this voltage source and P two is the power at this voltage source. All right, so, um, p one is equal to on, you know, from previous video that power is equal to voltage multiplied by current. All right, so what you need to notice is the direction off the current flow. If it's entering at the positive terminal, then the power is positive. So this will be positive. Different entering at the negative terminal, it will be negative. So the answer to this one is two volts, two multiplied by three amperes. That would give you answer off six watts in this example here. The current is entering at the negative terminal off the source. So p two is equal to negative. The times I, which is equal to negative two multiplied by three on that negative six. What? That's just a little trick you guys need to know. I mean, you look at the direction off the current flow when calculating the power off these sources . All right, this is the next example. Were also is to calculate the power often element at time is equal to one second. If the voltage across it is minus 10 T Millie volts on the current through it is to e to the power of minus 40 milli amperes. So once again, we use the power formula. So power is equal to voltage. Multiply it by current V is equal to minus 10 t on that in medieval multiplied by two e to the power off, minus full T over there. Milly on piers. All right, so if we just multiple this together and substitute T is equal to one second So that 10 one believe old multiplied by to e to the minus four minus four times one minus full 1,000,000 piers, that will give you an answer off minus 0.37 micro. What's if you're just confused? Why, it's micro ticket. It's because you have a 1,000,000 over here, which is times 10 to the minus three and amily over here. That's also a times 10 to the minus three on the in. Terms into the minus three times 10 to the minus three is equal to 10 to the minus six, and then we all know that is equal to micro. All right, so that's why we get this micro over here. If you get confused doing it like this, how I would recommend you do it is you convert everything to S i units. So you'd keep this involves and that in on Piers. And then your final answer will be in Watts. It's just, however you find it most convenient to do it. 4. Kirchoffs Laws: There are two main kids jobs. Current laws that are used in this module that is Casey. Oh, and que vio Firstly, keep jobs. Current law states that the some off current entering and leaving a note must equal zero. So you have, for example, all the current going in must equal the current going out. So I won, plus I two plus I three is going in, which is equal to zero because zero is going out. There's no our killer currents over here we have I one plus I to going in, and we have I three going out. And here we have no current going in. So we have I one plus I to plus I three going out que troves. Voltage law states that the summer voltages around a closed loop equals zero. That's for both clockwise and anti clockwise. A little tip. You must always be consistent with the direction choice. You choose each example, so each loop you must either choose for all of them to be clockwise or all of them to be anti clockwise. So let me do an example. So you could understand what I'm saying that, um, this example It says. Generate three equations using Cavey automation anuses. So have by one I to and they will have The third equation will be off the independent loop , which is all the way around. All right, So to find the to do que vio for loop, I won. We start off with the here and a cozy not negative off the off the voltage source because negative six, the impassive sign convention states plus three i one on the reason that three times I is because voltage is equal to current times resistance, um, cause so that this represents a voltage. So we have minus six volts plus three homes multiplied by the current, which will give you voltage and then moving down here plus 10 I won minus I to equals zero . The reason I have this minus I two is because we have current in this other mish which is flowing in the opposite direction off this 10 or resistant. So that's how you have to write it out now to do que vio for dupe I to we will start your past the sign Convention states positive. Negative. So it's positive 22 plus 10 multiplied by. I two minus. I want equals, Zahra. So that same thing that we did over there, just the other way around? Because, um, we working on the other side off this resistance? All right, um, to generate 30 equation. You follow, Um, the the independent lip. So I follows this part here also in the clockwise direction. All right, so you're start. Call this. Do you? Um three. All right. Said insist their negative six plus three I won. Plus 20. High, too, equals zero. They generally would be no need to, um, formulate the stood equation. People's over here. We already have two equations on day, two unknowns, the equations to our nose. So the only reason we did this over here was just to show you that you can do que vio for an independent loop. 5. Types of Sources + Branches, Nodes and Loops: in this video, I'll be discussing the types off sources you get in circuits on our then discuss branches nodes on bloops. Andi hard to count or identify the in circuits. All right, so if you have a diamond shape with an arrow, it's a dependent current source. If it's a diamond shape with a plus and a minus inside it, then it's a dependent voltage source. If it's Ah, circle with an arrow, then it's an independent current source. Andi, if it's a circle with the plus and minus 10 it's an independent voltage source, all right, so you can just remember the diamonds referred to dependence. Andi. The circles refer to independence. Then the arrows refer to the currents and the plus and minus referred to the voltage. All right, Now, what is the difference between dependence on independent sources? Basically, it will be given to you like this in the circus, and they will be labeled with a value, right? So if it's a dependent source, so it has a diamond shape. Then it will be a new miracle number multiplied by a letter with a subscript. All right, then. You know this I one is a value somewhere else in the circuit, possibly a current flowing through a branch somewhere else in the circuit. Then you need to calculate that I won and then substituted into here, and then you'll get the voltage value off. This independent are sorry off this dependent voltage source, so basically it depends on another value. That's why it's called dependent, whereas independent dozens depend on another value. So it's just 30 votes. I noticed the lack of a subscript there, so it's not city multiplied by a voltage. It's just 30 volts. So you just need to keep an eye out for the sub scripts. All right. Branch versus Node versus Loop A branch is a single element. Example. A resistor, a voltage source, etcetera. It could be any element in the circuits. It could be a current source, independent current source. It could be a capacitor. And in dr anything like that, a node is a point off connection between two or more branches. So just note. If even if you have two branches in Siris, um, like this, then there's a node between there. So the point of connection between two or more branches All right, Um, now, you get two types of dupes, you get a normal loop. We're just a loop on, and then you get an independent loop. Our first explain what a normal loop is basically a normal loop. Um, would look something like this so that that's a normal duped. As it passes through. I'm a bronze like that that it's also, um, a normal dude on. So is this could pause through more than one brunch. All right, so that's why they normally put look like, whereas an independent loop, dozens cross any branches. So in this case, is a independent group there the and there. So then we have. So that's the difference between the normal dupe writes on the independent route. Independent lips don't cross through other branches. All right, then we have this formula with a number of branches is equal to the number of nodes, plus the number off independence lips. So that's a number of independent lips, not the number of normal loops minus one. All right, this formula is used for a question where they ask you to count the number of branches, note and loops, and you could use this formula to test if you are right or wrong. All right. So if we have this example here, it asks us to determine the number off branches, nodes and independent loops. So we know the branches almost easiest to calculate, because you just can't the number of elements. So then it would be 123 full. 56789 So, you know, the number of branches is equal to nine. The number off nodes as equal to so we know a node is a point of connection between two or more branches. So that would make this a node over here. That's a node. That's a node. A point of connection between two or more branches. Yeah. Isn't another massive node, right? It's a point of connection between two or more branches. Then we have another one here. All right, so that should be all of them. Because, you see, those are two projects, so that's point of connection between two branches, so that then you count them. 12345 So then we have five notes, then the number off independent loops is one to three full five. So now we can check our answer by plugging it. It plugging it into this formula B is equal to N plus o minus one nine b equals five plus five minus one, and therefore nine is equal to nine on, therefore your answers all most likely to be correct. All right, so that's how you determine the number of branches, notes and independent loops. 6. Cramers Rule in a 3x3 Matrix +Example: Hey, guys. So this video, we grain too show you hard to solve a two by two or three by three matrix using Cramer's rules. So basically, they would give you a set of equations on. Then you have to use Cramer's rule in order to solve for the variables. So, um, to calculate the determinants or two by two matrix, you say a multiplied by D minus be multiplied by C. This is just a formula you need to know in what you use Cramer's rule. And then you also need to memorize these formulas in order to solve for the variables v one , v two and V three. So to do an example solved for heat to All right, So something you need to know for Cramer's rule. It's just the following matrix with positive and negative signs. We'll see where we use this in just a moment, right? So you first start off by writing off writing out the coefficient matrix. So for the one that's full to be two and 03 minus to B one is early to one B three one. You want to be 203 All right, this is just the notation off your write it out in the Matrix because the answers ones, there are one Morocco. So you start off calculating d determine it off this crayfish in matrix. But I like to do is I like to choose the road with the most amount of zeros because that'll simply fire like you'll be able to calculate the determinants a lot quicker. So in this case, or fears have the same amount of zeros, so just work with top, right? All right, so you start off positive for multiplied by two by two matrix. He cover fours Carla Monroe and you left with They're one to their at their 120 All right. Minus two minus two. You cover it's column and road, and you left with Monness 2110 plus zero plus zero multiplied by its, um minus two 01 to, uh, But this doesn't really matter, cause zero multiplied by anything is gonna give you zero, so you could just get rid of that. So now you calculate the determinants off Two by two matrix, which is the formula. I should be here, so it's four multiplied by. There are times there are minus one times two, which is minus two. It's in a good two multiplied by minus, two times their a minus one times one give you negative one. All right, then you left with negative AIDS plus two, which is equal to negative six. So d is equal to negative six, but yeah, just use formula here. Negative six will be substituted. They they they All right. So the question asks us to find view too. So that means we are required to calculate detail rights. So coordinated. Do you need a nuclear fission matrix? And you substitute, um, the answer into teacher's college. So you want to be three? So this column represents the one that comes to Macron V three. So you substitute 10 And why into btu's column? One there, one on that just made the same. So it's full negative. 21 They're 10 All right. So now I can find the internets d to you do it the same way. Positive for for the full multiplied by their times. There, minus one times one is negative. One minus one, right. Multiplied by negative to time zero, Which is there a minus one times one native one plus zero. Plus, there are multiple calls, something just gonna give his era. I can't minus full plus one, which is equal to negative three. So using Cramer's rule formulas every year we caught late in Teacher Teaches people to D two D, you two is equal to negative three. He is equal to negative six. The kitchen on so 0.5 holes, right? So if you wanted to calculate the one, for example, you just substitute these answers in TV. One's column in the columns for Beats and VT remain the same, Then calculate the determinants on. You'll get an answer for the one on you. Substitute. Do you want into this formula? And Devery Guinness? Negative six, As we calculated before, and then you'll get your answer for you. One you could do for the same procedure to calculate Vetri. 7. Passive Sign Convention + Example: in this video, I'll discuss what passive sign convention is, and I'll do some examples to illustrate this. So basically passive sign convention states that current flows in a voltage drop direction , so that is from the positive to the negative off the source unless otherwise stated. So if you given any example like this here, you have the source. Um, basically, it flows from the positive to the negative of the source. So we're doing que vio you could do it like this. It Ince's up the negative Negative? Sure, volts. Negative to then over here. Plus three I won plus, once again flows in a negative drop. Duration plus five i one equals zero. And then you can solve for y one. If we look at this example over here, um, once again moving clockwise, I won. And they're negative, too. Plus six I one because that's passive sign convention. But in here it's otherwise stated that it's negative positive. Then you say, minus five volts because that's five votes equals zero, and then you can so, for I want 8. Series and Parallel Resistors: in this video are comparing contrast Siri's and parallel connections off resistors in circuits. So just little thing you guys do, you know, if the very of a resistance equal to zero, then it just becomes or you treated as a short circuit like that. So it's like there's no resist in between the cables on. If the resistance is equal to infinity, then it becomes an open circuit, just like there's not even a resistant in between the wires. What is a serious connection? It is when two or more elements share a single note exclusively, two points that are very important that you need to know. And I used very often when problem solving with the circuits the first is current will be equal and voltage will split. So if we have the falling resistors, the current's flowing through or one or two in our three will be equal. But the voltage across our 1 may not be equal to the voltage across our two, which may not be equal to a voltage across our three etcetera. All right to calculate the equivalent resistance, Um, you just add the resistance if they are in Siris, so as you can see here. Resistance equivalent is equal to R one plus or two plus or three plus are in, um all right. And Oren's just like more resistance. Right? Parallel is when two or more elements are connected to the same two nodes. Two facts you need to know about this is that in parallel, the current will split Andi in parallel. The voltage will be equal. So if you have the falling circuits, the voltage across this branch and this branch and that branch would all be the same. But the current across or one may not be equal to the current across our two, which may not be equal to the current. Across our in so current splits in parallel, but voltage splits in Siris. To calculate the equivalent resistance, you use the reciprocal reciprocal of all the resistances and you add them together. Once you've added them all together, you just flip the final answer to get R E Q at the top. And then that will be the value of R e que in owns. So over here we have labeled with a little read Asterix Um voltage will splits for Siri's and current will split for parallel. Basically, there are two formulas you could use to calculate this. It's called current division for this one on Fort. Each division for this one. Um, that video will soon follow off to this one. 9. Series and Parallel Resistors Example: in this video, I'm going to do an example to calculate the equivalent resistance of the circuit. So this question tells us to calculate R E Q and R E. Q is over here between these two points, all right, and osos to calculate Arctic you win R is equal to zero. So that's when these two are values are equal to Zahra and when R is equal to infinity. So we're gonna have to scenarios to answering this question so we'll start off when R is equal to Zahra. All right, so we learned in the previous video that when the resistance is equal to zero, then it becomes a closed circuit. So if we redraw the circuit, it will look like this. And here we have the closed circuit. All right, so you'll notice I didn't draw this six own resistor. And that's because the the this cable over here on this wire short circuited this resistance and then you just treated as off that resist is not even there. So if I could just clarify that for you, if you have a resistant between two points A and E and is a wire going around it like this . You call that a short circuit, call this a short circuit, and then that is treated the same as this. So it's as if the resistance is not even there. All right, so we can now calculate the equivalent resistance, which is R E Q. Over here you will notice that this resistant and this resistor share the same two nodes, so they are in parallel. So then the resistance off four parallel with five is equal to 1/4 plus one of the +51 of the four plus one of the five is equal to 20/9. But you still have to flip it cause that's one of our parallel is equal to 20/9. And then that because in our parallel is equal to 9/20 homes. All right, so now if we redraw the circuits, it will look like this. And then we have our G Q over here of 10 3 9/20 Now you'll notice that these three resistors or in Siris, so to calculate R E Q. Say 10 plus 9/20 plus three that gives you an answer off 13.45 homes, all right. So this is for win R is equal to zero. So now, to calculate, um, the r e que When r is equal to infinity, we could then make these two resistors an open circuit. All right, so if we had redraw the circuit, it would then look like this. Yes. Are you Q. You have our five resisted. Here are 10 urn are three. I'm four. Yeah, we have our six. All right, so it's the same as this, except it's as if this cables not even here, because it becomes an open circuit. So you left with just that, All right, so now we can go and simplify this the circuit so we can see these time in Siris. So it's six plus five, and you didn't just be left with a resistant off 11 arms. All right, so it's as if that's not even the anymore. No, this 11 homes and this forums are now in parallel. So then the resistance, when for his parallel with 11 is equal to one of the four plus 1/11 can punch the singer calculator one of a four plus 1/11 that's 15/44 But then, remember, could it's parallel. We still need to flip the answer. So once you flip, it will get 44/15 or right? So then we're now left with a circuit that looks like this. We have the 10 home, the three home on 44/15 the You'll notice that these three resistance are now in Siris. So our e que is equal to 10 plus 44/15 plus three. So that is equal to 15 comma 93 bones. So that is our e que for the scenario when R is equal to infinity. All right, I'd recommend you Jessica, practice some of these examples. It's not too complicated. You just need to, um, basically simplify the circuits you need to see when they are in serious when they in parallel, and then just apply the formulas and get your final answer off R E Q. 10. Current Division and Voltage Division + Example: in this video, I'll compare and contrast current division on voltage division on of into an example. All right, so current division is only four, um, parallel branches because current splits in parallel on current stays the same in Siris, so there's only applies to parallel branches. So basically, if we have a circuit like this and we have to resistance, we have a current source. The in the current will split in different proportions based on the fractions off the resistance. All right, so this currents going down here, I won, and I to If you add them together, you will get the currents off the source. So the inputs, So just like doing Casey? Oh, in is equal to art. So the current source going in is equal to the the currents that splits going out. All right, so that's what that formula this is. Ice is equal to R one, plus I to then to calculate I won. That is equal to r two. Divided by the sum of all the resistance R one and R two multiplied by. I s the current of the source. I to you do the same thing except the numerator has are one instead of our two voltage division only applies to Siri's connections. On this is because voltage splits or divides in Siris. So you'll have this circuit year with two resistance on the voltage source on the voltage across. Resist the one and the voltage across. Resisted to will change depending on the fractions or a shows off the resistance. So to calculate the voltage across our one, you say resist the one the value of resistant one divided by the value of resistant one plus resisted to. And then you multiply that by the value of the voltage source so we can do an example. This question Osos to calculate I won, so you'll notice that I want is a current going through a branch which is parallel to another branch. So that should immediately make you think that you need to use current division. All right, course current splits in parallel so we can calculate this by doing Casey Oh, at this node over here. All right, so we know Casey, all we say in his equal to art going in, we have nothing here. We have I one going out, so that means our to it or should be going Answer zero and doing art is four amperes with six amperes on. We have the I one coming out year. We could call this I won and that I to so together we'll just call it I s all right then I s is equal to minus 10 on piers. So no, How this can be looked at is can be looked at as a current division. So to calculate, I won, he used a formula or two of or one plus or two multiplied by IHS. Then our two is equal to full or one plus artist three plus four multiplied by I s, which is minus 10 and that will give you an answer off minus 5.71 and piers, All right, just to clarify something to you guys, the current's in actual fact is flowing in because we know, According to this formula, workers in must equal to workers art. So if four and six is going art, then something needs to be going out at this node in order. Something needs to be going in at this note in order for this to go out. So basically, I want a night is actually flowing inwards. But because the question told us I once flowing this way, my final answer would be a negative value. But if this arrow was facing upwards, then our final answer would be a positive value, because the I s would be positive. Andi, That's because this i s would now be on the in side of the equation. I hope that didn't confuse you guys too much. But if you just follow this method, you'll get the right answer. I was just trying to explain to you that this is not the actual direction off the current flow of I one. 11. Wye Delta Transformation + Example: in this video, we'll be discussing why Delta transformation. All right, so why don't the transformation is basically a circuit simplification technique? So if you have a circuit Andi, your trying to calculate the maybe the equivalent resistance. Andi, there's nothing in Siris or parallel. You might hope to transform from the why to a daughter or from the Delta to the Why formation in order to be able to simplify the circuits. All right, So this or one or turn or three would make up what would look like a wide formation, and our A, B and C would make up what looks like a adults information. So you would use the falling formulas to convert from a wide to daughter Formacion. You'd have to memorize all these formulas. All right, you'll notice the difference between the three formulas is the denominators Differ, Andi, the numerator czar. The same or one corresponds to our A and then B two, or to unseat or three. So that's just the last way to remember ABC. 123 All right. Just a little hint if our one is equal to R two, which is equal to R three, for example, If it's equal to 10 owns then, or a B and C is equal to three multiplied by or one andare ones, the same as or two or three. So you just say three month supply by 10 and that equals city owns, and obviously save applies vice versa. If you given its indulge a formation or a B and C and or A, B and C are all the same value, then you divide that value by three to get our 1 to 1 or three. All right. But if they are not the same values, then you use thes formulas for Whitey daughter or these formulas for Delta to Why so the denominator is the same in these equations, and the numerator is differ. Um, you'll notice are a is missing here and are a corresponds to our one here. R B is missing and RB corresponds to our two. So you know, it's just some easy ways to try. Remember it, you know, So we can now do an example. This'd is the question find are cute. All right, So, um, the first thing you do is try find what's in Siris and what's in parallel, and then you just simplify it down till you left with one resistant. So we'll see here. That 60 and 14 Siri's. And so is 10 and 90. So we add that we get 100 at that, we get 100 and then you'll be left with a service that looks like this. All right, just the black part. So you'll notice now that nothing else is in Siris or in parallel. So that is why you'd use why Delta transformation. So here we have a why. Or you could use this why? But I'm just going to use this one. Andi, you converted to the Delta transformation. All right. So, um, what we did then is because thes three values are the same in the UAE. Information you just multiplied by three to get our A, B and C as mentioned before. So then you'll have a circuit like this. This hasn't are being transformed into the doubts of formation. Your non notice that this 300 homes on that 1 20 terms shared the same two notes. So the snowed here on this note here, So it makes thes two in parallel. So you calculate that 1/1 20 plus one over 300. You flip the final answer. You'll be left with value that looks like this. 600 divided by seven. So you'll notice. This is also in parallel, so you do the same thing here on being These two are nine Siri's, so you can add those. All right, then you have 1200 over seven. If you add those two resistance and now these two resistors are in parallel. So then you just calculate this So you do that one over. Oh, are it's kept. Quarter or equivalent is equal to one over 1200 of a seven plus one over 300. You'll get your final answer, and then once you flip your answer, then R E Q would equal to 109 volts, and that would be your final answer. 12. Nodal Analysis + Example: Hey, guys, In this video, we are going to do a nodal analysis example. So just some background knowledge. You need to know how to use Casey O, which was covered in a previous video. If you just want to recap that quickly on homes, raw formula, eyes equal to the higher voltage minus the lower voltage divided by R. So this is illustrated over here. So what? This basically does. It just helps you to choose the direction off the current float. That always goes from the higher to the lower voltage. To do an example, I'll keep the formulas above here so you can refer to them as I go through it. Um, what I like to do with problems like this is I always like to define the direction of the current beforehand, so I don't make a mistake. So the example we have to do is set up to equations to find V one and V two using nodal analysis. So we have you in here V two there a to these two notes, so start off at the one. Right, so we can see current flows in this direction by the source. So it goes in wits over there. Um, of here, we actually have a ground. All right, so the voltage at the ground is equal to zero. I get. So obviously the voltage would be high here and lower here. So the current will flow this way, the then there's a trick. You can either choose for the current to flow in that direction, or you could float, so you can either choose for it to go out or in it will give you the exact same answer as long as you consistent. So show you where you have to remain consistent. So basically, I'll just assume it flows up. All right, then. No. Two. It's going out over here because of the direction that arrow going in over here to the direction of that horror. And it's going out to the here because higher and lower explained area. Basically, it goes in here because we said it comes out of here so close enough here, Const Acres. The current flows in this direction of the here and in that direction of a here, you must just remain consistent for birth notes. All right, so the way I like to do it is to do, Casey. Oh, within equals out So restored at node of you one. Right. So in we have three MPs and out. We have well started here how we have B one minus zero. So it's the voltage higher minus 40 to lower. Divided by R In this case, the R is equal to the three resistor like a plus. If you are minus V two, divided by two right then we go at V two. So this is the question done for the first mode. The question for the second note in is equal to five years. Five plus, we have another interview here. Had to Samos this formula you want minus V two brought about two. All right equals ox, which is the three amperes. And out here, which is the V two minor. There are over four. All right, so these were your teak razors there see equations and two unknowns. So that means you can use either Cramer's rule or or just simple simultaneous equations and soulful B one and B two. If you're solve, you wanna be too the one we're equal to 8.66 on V two with equal to 8.44 All right, so if it confuses you like which direction to choose? Just know you can choose any direction between the one and V two, but the trick is, if you choose the current to float this we rights instead of that way, you will still get the same answer. But instead, let's say over here beats the V two formula because it's going out. So you drive from this side and you say plus V two minus view one V two minus view on higher, minus lower because you're assuming this one's higher on this one, so divided by two and then on this side it would be the same thing to minus you one or two and then that on that would not speed it. And they basically you have two different equations because you chose different directions off current flow. But the answers were store remain exactly the same 13. Supernodes + Example: Hey, guys. So in this video are briefly discussed super nerds, and then I'll do an example. So this is what I call nodal analysis with voltage sources. So if there's a voltage source between two nodes off the circuits, then that voltage source becomes a super node. So, yeah, that's how have indicated yet occurs when there's a voltage source between two notes. Another thing you need to know is any resistance parallel to this branch can be ignored. It doesn't have to be, but it can be. And thirdly, you'd use Casey O on the potential difference formula in order to on derive formulas to solve the unknowns. So this potential difference formula here it is V s equal to be positive minors, you negative. So the voltage source, which is six volts equal to view to which is, on the positive side, minus V one, which is on the negative side. Then this would become one off the equations to solve for your unknowns. Example. Um, you'll notice that they don't tell you to use. Use a super note to solve the problem. You have to figure it out for yourself. So how did you figure it out, you will notice that there's a voltage source between two notes on. Then you know this is shoot a super note, so you have to just have an eye for that just either from knowing or just practising examples. This voltage source year does not become a supernova because it's connected to ground. So that just means V one is equal to 20 volts. Dr. V. One is equal to 20 all right. The potential difference formula said the voltage of the source is equal to the voltage of the source is equal to the voltage at the positive side, minus a voltage of negative. So basically that's four is equal to two minus the three. All right, so have you run? We have this formula. Yeah, and now we can do nodal analysis treating this voltage source as a super note. So let's start off saying in must equal out. So what flows into the super Node? Backers are backers are backers arts, but this goes in, Ifo goes in over there. Right? So that's view ar minus 33 over six. Using that formula eyes to be age minus vo, divided by resistance. So the high voltage minus the low voltage. This was done in the previous video. If you just want to go get a recap on that that's in equals out. So what? We have the three over five basically the same V three minus zero, cause the voltage at ground is equal to zero p. Three months there, over five. Plus the two minus zero over 10 on. Plus, I need to minus view on forever one. Andi, There you have it. So you have It's your nose view one And you are the two v three and then you What we know is 20. His substitute 20 There. On there you have two equations, two unknowns and you can solve simultaneously on get the value off B two and three. 14. Nodal Analysis by Inspection + Example: in this video, I'll discuss nodal analysis by inspection. All right, so you can use nodal analysis with our king inspection if you want, because this module requires that he only answer on the answers without showing calculation . So you could just do normal motile analysis. But by learning the inspection method, it's a lot easier to solve very complicated circuits. All right, formula you need to know is G is equal to one over r. So it's the reciprocal of the resistance. And then you can only use nodal analysis by inspection if all the sources are independent current sources. So it's that little independent current source. All right, so we have an example to find V one and V two. Okay, So here we have the circuit with all the resisters. Then I calculated g of all of them, which is just one divided by r. So one divided by 20.5 etcetera. All right, um, then you sit up the falling matrix. All right, Andi, there's one in one refers to node one, and this two and two refers to node to over there. So to get the diagonal elements, which is the diagonal this way. Um, you you are the some off the G's connected to that note. So let's do that. So we're working with mode number one over here. Some of the cheese connected to that note the G connected to this note is one one on day, 0.5 plus 0.5. All right, then, for the Stagno. No, to we have one plus 0.2. I can't. And for the off diagonal elements, the value is a negative. G between the two knows. So we have these two notes on the G value between the two nodes is one. So it's with negative cheese. So that becomes a negative one on negative. What? All right, then, for the the answer on the rights inside the son of the currents entering the notes. Um, if the current sources going into the node, that's positive. And if it's going out, it's negative. So four night, Why in its positive? So it's plus three and then going out this negative minus five, that will give you an answer minus two. And then over here we just have in five sets. Just positive fun. So there you have it, then you just add that together 1.5 on 1.2, and then you can use Cramer's rule to solve for V one and V two on the answer. To be one if you use. Cramer's rule is three 0.25 volts on V two is equal to 6.88 volts. So you can you can go watch that Cramer's Rule video. If you don't know how to use Cramer's rule, or you can just simply solve these two simultaneously, and it will give you the same answer. Awesome. 15. Mesh Analysis + Example: Hey, guys. So in this video, I'll be discussing Mission Alice is on. I will give an example. Formation and assist. You use Katie. Oh, you use law e equals a times are so well defined. All the voltages in terms, off current and resistance on. Then if a current source exists in only one mish, then that current is known. So this example here asked us to solve I one i 23 and four. So now that's the current in each mish for us so we could start. That's I want All right. So way clockwise and you stay consistent for all the measures. All right, we'll start you. So you're entering at the negative. So it's negative. 22 volts plus minus, um, plus 31 plus to I want right, But notice now that there's also a current flowing in the opposite direction to I won. So are ones may be down, but I two is moving up. So you're actually saying minus two All right, too. Then that will equals era. That's just basic que vio as covered in one of the previous videos. All right, so then you can do I to which is this one, so we'll start off, um, two multiplied by I to minus. I want. So that same thing is what was going on here? Just the other way around, then. Plus, there's another two runs here to I to minus full. That's the I four hitting opposite direction. Um, plus five times I to minus I three, because there All right. Uh, three. 123 for us. That's five rooms, right? We're going up this way. Five homes by I three minus. All right suit plus seven homes over three plus nine. Supplied by three equals there for on. As you can see, there's a current source in the scoop on as mentioned earlier, a current source exists. If the current source exists in only one mesh, then that current is known. So I fool then equals three for us. And then they haven't. You have four equations for nights on end. You can then use cream is rules. Uh, any other method you like to solve for 1 to 4. Just a little thing here if this current source was facing the opposite direction. So the arrow is pointing that way. Then I four would you call negative three? Um, yes. And they also if you once you define, like, if you wanna do mission at assist, like through the entire if you can. Life where I'm trying to say is you could also do mission analysis, uh, through you know, like that. But you don't necessarily have to. You just have to kind of just look at the circuit and figure out which missions you want to work with. That will you have the simplest equations to solve for the variables? 16. Supermesh: in this video, I'll be discussing some tips for super missions and I'll being doing example. So tip number one you must always do case yell at a node by the current source. Number two. You use a super mish when there's a current source that exists between two measures. So to show you what that means. If there's two missions like this, Um, and there's a current source between it, they invest here, becomes the super mission, and then you treat the current source as negligible as if it's not even there or rights. Then the third step is it's can be worth or with art, other elements example resistant. So that will become more clear to you when I do the example. So has example, this question asks you to find I one i two and I three. Um, now any test that they're not going to tell you what technique that you need to use to find it, but you know, because they're asking for currents, you know you need to use mission analysis on because thesis ah, current source between two loops. You know that you have to use a super mish, So the super mish we'll follow. This path was down around here, creates a new mish like this in the ants acting in that direction, all right. And then he basically can treat this current source and this resistor as if it's not even there. That's what I mean by can be with with art, other elements. Example, a resistance I get so we can now define the directions off the current flow. One I to and I three just remember to remain consistent with the direction you choose, they must either all be clockwise or B anti clockwise, so I'll start with I to rights. So, um, going this way we start to multiplied by to plus five multiplied by I to minus I three because I three is acting the UPS direction plus living on up here three multiplied by two minus one. That equals zero. All right, now we can do the same thing full the loop off the super mish. She put she commission morons. So we'll start going up here on that minus five faults minus five. Moving down here. Plus three multiplied by I one minus I to iTunes acting in the opposite direction. Over here plus five I three minus two, then moving on, going down to this resistor plus eight i three and then that's all the elements equals zero all rights. But as you can see, it's only two equations, but three unknowns. So then that's what I said. You use, um, que CEO at the notes by the current source, so you can either use the snowed or this note. So I'm going to use this just cause it's easier. So you do. The in equals out, so I one is exiting here. I won on I three is entering here in The seven appears is entering. So in would then be seven. Plus I three equals I one. Then you have three questions. Three hundreds, and you can then soul simultaneously or using Cramer's rule, and you'll get the values off. I one I two and I three 17. Supermesh + Example: in this video, I'll give you some tips about super missions, and I'll then do an example of how to do one. So how do you know when to use? A super mish answer to? That is when a current source exists between two measures. So like there's two missions and then there's a current source between the two, all right and they can be could be with with art, other elements. Example, a resistor. So basically they could either be just the current source score. There could be a resisted as well. So that's just something you guys, you know, just so you don't get confused about a resistant. All right, then here is something you need to know for how to how to calculate these formulas. So when you have a super mish, you can you can write off for this example, I tu minus. I want equal seven. So I two is positive because that act in the same direction as the current source, which is that way upwards. And then I was negative because it acts in the opposite direction in that equal seven, which is seven, and piers, which is the value off the current source over here. It's the same thing except the current sources acting in the opposite direction. So then I one is positive because it's acting in the same direction and I choose negative. What is acting in the opposite direction in that equal seven. So to do an example, um, this question asks us to find I one I two and I three. So the question won't tell you. You have to use a super mish. You have to figure that out for yourself. So the reason you know you have to use a Superman is because, um, as a current source there, so you can draw a super mish little acts basically over here like that. So we'll just cool. We'll call this Lupita. I one, we'll call this one I to and this one three. All right, so, Teoh, start if you do, Katie Oh, on. We'll start with this simple loop over here. So loop I to so two times I to plus five homes multiplied by I to minus I three because I three is acting in the opposite direction. Plus three OEMs that over there three arms are deployed by I two minus. I won equals era. Now you can do the loop for the Super Mish Commission. All right, we'll start over here. Going upwards, sauce. Negative. Five. Remember to stay consistent with the direction. Archers Clockwise. So our searchers clockwise? Yes. You should stay clockwise here because negative five volts plus three, one minus two plus moving down here. Five I three minus two plus moving on down here. Eight three equals Zahra. So I'm sure you noticed with the super Mish, you just assume that this entire branch or both these branches just disappear. So this this resistor on this current source you just treated as if it's not even there. All right. But now we only have three equations with three unknowns. So in order to get third equation, we use what I was showing you earlier with this. This technique, basically all you do, as you say I won. I want cause it's acting in the same direction. So it's positive minus I three minus, I three could acting in the opposite direction to the current source equals the value of the current source. In this case, it's seven and piers seven. Then you have three equations on three hundreds and you can solve using Cramer's rule 18. Mesh Analysis by Inspection + Example: in this video, I'll discuss Mission. Alice is by inspection on Do An example so you can do Mission Alice with our inspection. But by using the inspection method, it's a lot easier to solve larger, more complicated circuits. Formation. Alice is you use the resistance. Um, but nodal analysis. You use the reciprocal of resistance, and then you can only use mission analysis by inspection if all the sources are independent voltage sources. So that's the symbol for an independent voltage source. So the question or the example tells us to find I won and I to. So here's the circuits. What you can start by doing is riding out the Matrix. I then, to find the diagonal elements in this matrix, which is these values going along this diagonal? Um, you some the ours in that loop. So if this is loop, warn that sleep too. Got sleep one that's true, too. So we'll start off by finding the some off the resistance in loop one. So Loop one, we have resisted their three plus four, all right, And then over here for, um, live to you. They have full plus five, all right. And then for the off diagonal elements, which is these values, Um, it's the negative are off the resistor between the two loops. So basically the negative off our between loop one and loop to is negative for on between Luke two and Loop one. That's the same thing. So it's negative for all right, the the answers on the right inside on. Do you find the some off the voltage off the sources? So for I one, you do it for I one. And therefore I, too, for I one. Um, just note it's in atnegative. Then you make it positive, and if it's in a positive, it's negative. She goes like this. You go in at the negative, then becomes positive six on for loop to its in at the positive, so it becomes negative seven. So it's literally the opposite off what you usually do when you do que vio Um, so that's basically how you do met mission analysis by inspection. But if this is Austin, the test will be a lot more complicated. Example. Because that's a point off doing it by inspection, it's to be able to solve complicated circuits using a simpler method 19. When to Use Nodal or Mesh Analysis: Hey, guys. So in the semester tests and exams, the the question does not told you to use nodal analysis or to use mission analysis. You basically have to figure it out. So it's easy once you've done plenty of examples to figure out which method to use, but of just middle summary here off. How to identify whether to use notable omission. Anuses. So basically love thumb is that you want to use the method that will yield the minimum number every creations. So how do you know which method will yield the minimum number of equations? You can look at thes three points thes three of the same points. They're just basically the opposite. So you use nodal analysis when a circuit has more measures than nodes, whereas mission analysis you use when there's more nodes than measures. All right, if you need to use a super node, obviously nodal analysis. And if the circuit requires a super mare, she used mission analysis on just a general thing. I picked up that if the question asks to find the voltage, you would use nodal analysis on if it asked you to find the currents you would use. Mission Alice is I hope that will help you guys, too. Figure out when when to use which analysis 20. Transistors: you guys send this video, be discussing the theory behind transistors on, give you some tips and tricks for how to go about doing these questions. Um, this video does not involve any examples. Examples will come in the next video. This video's merely to explain the theory and formulas involved with transistors. All right, so this is the symbol of a transistor on. If you see this symbol somewhere within the circuit, then you know that it's a transistor question. So transistors made up of a base and emitter and a collector where there's a voltage or potential difference between each of these between the base and the matter, you have VB between the collector and emitter your VC. Between the base and collected, we have the C B. All right, so if you dio que vio around the around the transistor, you'll be left with the following formula. We see you is equal to VB plus V C B. So you could just manipulate this formula to how you like for depending on the question. All right, then, there's also a value in, you know, VB is equal to 0.7 now. This value would usually be given to in the question. But if it's not, just know that VB, which is this value here, is equal to 0.7 volts. All right, so moving down, we have, um, the following formulas. This formula here is determined by doing Casey. Oh, because I see and I be are going into the transistor and then i e is going out. So then that's where we get this formula from on the the rest of the formulas you just need to memorize. It's basically just defining one current in terms of another, currents multiplied by a constant. So what this constant beat a means is it's a Commons common emitter current game. It's a value between 50 and 100 and then the constant offer is a common base. Currents gain value between 0.98 on a 0.999 so you'd use these formulas when you want Teoh simplify in equation. For example, if the equation is written out in terms of I see and I e. You could rewrite Icy and I in terms of I B. If Peter is given on, then you'll only have one unknown and then you'll be able to solve for i b and then further soul for I see and I e. We will get an example with that in the next video. Then we have a equivalent network model. What this is it's exactly the same as this that I showed you earlier. It's exactly the same as this. So you see the position of the base B, C and E is the same connection points as B, C and E in the equivalent network model. All right, so you'd usually redraw the circuit, replacing that transistor with this equivalent network model. It means the exact same thing. And you'd usually do this when you are using notable analysis because it's very difficult to do nodal analysis with this, Um, and it's easy to do nodal analysis with this. So if you're doing mission Alice ISS, you would just keep it like that. And if you're doing notable analysis, you'd converted to that. So, um, that's pretty self explanatory. We just have a dependence current source of the voltage source on There's the directions of all the current flows. So once again, VB is equal to 0.7 as mentioned earlier, so we will get to an example. In the next video, I would recommend watching that video because it'll explain quite a lot of the concepts involved in transistors. 21. Transistors Example: Hey, guys saying this video do an example that covers most of the concept off transistors. Um, this example asks us to determine Visa and V c. So that's Visa and V C given VB, which is equal to 0.7 votes so that there is equal to 0.7. And Peter the constant is equal to 0.99 So because they give us Peter, we know that we have to use these formulas which involved Peter. All right, so it means we probably going to be writing. I see, in terms of I b and I e in terms of i b So we'll get to that now. So because we know this is the the layout of the transistor that I be flows in And I see in an aii art I redrew that over here just so you don't get confused, I because in i C goes in and I eat goes out All right. So in this example would make more sense to do mission al icis rather than nodal analysis, because you simply just want to find Visa and V c on by doing nation Alice is in or que vio I would be a lot easier to solve. All right, so I'll start by doing que vio at the input loop. So that's this input clip. I just call it the input loop because that it inputs the transistor be here and in the art putting mets out here. So this is the Arthur Group. All right? So if we start by going up this way, we'll get negative 10 volts? No, because we entering at the negative terminal moving up is a positive there or passive sign conventional state that it's plus 20 on 20 k Don't don't write 20 and then make mistake 20,000. I be because you know that I be flowing in that direction. All right, then, moving down there. VB So it's entering at the positive, plus 0.7 VP is 0.7 all rights plus 200 homes because we answering at the positive Terminal 200 i e equals zero. All right, so here's the first equation done, but you'll notice that 200 i e is the same as V zero over here, cause voltage is equal to resistance multiplied by current. So that's what we doing. Um, of the hip. All right. So delicious, right? V zero is equal to 200 i e. All right. So now to write the que vio at the art put lip, we'll get a formula that looks like this be going up at the negative of you could start anywhere, but I just started Negative V c. That's one of the values you want to find. V. C. Then, um, it's negative over here. If these positive and negative not given to you, you need to figure that out. Using passive sign convention, you can go to recap the past a sign convention video. But basically, because the current I see flows in this direction, it flows in the negative flows in the voltage drop direction which will make this art positive and the side negative. So because we chose clockwise for the mission, Alice is, it'll enter at the negative, so that will be negative. 500 owns multiplied by. I see. Moving on. We come here to this point, which is plus 20 volts plus 20 moving down. Then he inside here, the negative terminal, minus 200 homes multiplied by I e equals zero. All right, so now you'll notice we have treat or three questions with many unknowns, which is I C V c on i B I e way have a lot more unknowns than equations. So then that is where these formulas fit in. All right, so or just rewrites these equations I see is equal to beat her times I be on i e is equal to one plus beater. I be these formulas you need to know off the top of your head because they don't give you any formulas in the test. All right, so we know beaters equal to 99. That will be 99. I be on this would be one plus 99. So that's 100. I'd be So now that we have I see and I e in terms of i B, you can substitute it back into these equations. So start over here with the negative 10. So it's a negative 10 plus 20,000. I be plus 0.7 plus 0.7 plus 200 multiplied by I e. On I e is equal to 100. I be and that equals Zahra. So you just want to simplify this because it's one equation. We have one unknown. Then there'll be 20,000 plus 20,000. That's 40,000. I be equals negative. 10 president seven. Then take it over to the other side. Get positive. 9.3. All right, divide 9.3 by 40,000 you will get a value off 0.23 to 5 Milli amperes. All right, so that's what I B is equal to. Sorry about that. I can Let's just do it like this, so you could see. All right, So now we substitute into this equation so we can find the value of V. C. Which is what? The question mosques or right? So if we simplify this V C E equation what is right, the CEO on its own, that would equal to minus 500 multiplied by the I C I C. Is equal to 99. I be plus 20 minus 200 multiplied by I e just i e Which is that 100? Be all right. It's Ah, Now we just have I'd be the unknown. So with I be equating to 0.23 25 times 10 to the negative three amperes. You'd only substitute with 1,000,000 piers cuisine. You might get your units mixed up, so just converted to amperes. You substitute that in there and then V c e equal three common 84 volt. All right, so that's V C. Now we still have to find V zero, so Visa is equal to 200 i e as we defined earlier over here. All right, I e we know is equal to 100. I be And, you know, I B is equal to 0.23 25 times 10 to the negative three. And then that would give you a finest final answer off 4.65 balls and there you have it. 22. Superposition + Example: in this video, I will teach you guys the superposition principle, the process on how to solve a problem using superposition on dial. Then do an example. So the superposition principle is when the voltage or current over an element is equipped, equivalent to the sun off the individual voltages or currents contributed by the independent sources in the circuit. All right, so the process to solve the problem using superposition The first step is you turn off all independent sources except one. So you turn it off by using one of these two methods. If it's ah, voltage source, Um, that could also be drawn as something like this. Right. Um, then it becomes a short circuit, and if you have a independent current source, then when you switch it off, it becomes an open circuit. All right, so that's the first step. So you turn off all independent sources except one. Then you find the current or voltage due to that source, you repeat the steps number one into for all the independent sources. And then lastly, you add all the results off those independent sources together. All right, so it's to an example this question here asks us to find Vieques using superposition. All right, how you do this is you just follow the process. So step one, turn off all independent sources except one. So you'll notice we have two independent sources. The circles. That's ah, dependence. Or so you don't look at that. You just look at these two independent sources. Single turn will choose to switch off the independent voltage source first. So that becomes a closed circuit. I'm just redrawing it just to make it easier, Um, when trying to solve the problem. So V X is a voltage at this node over here. So this year is a node, so we'll just call this V X one, all right. And they made me turn off. Um, this current source will call it a V X two, and then you just add the two together at the end. So it's calculate VX one. We do K c o at this node. All right, so that is the in equals to art formula. So over here, we have it going. Willis humans aren't here. Here's going in due to the direction of that kids going art. And here it's going in. All right, so going in. We have six appears plus 0.2 V X equals out. We have the X over 10 plus V X over five. Then if you solve this for Vieques. Oh, well, these old VX one. Sorry, then V X one is equal to 60 votes. So now the next step would be to turn off this current source. Alright, goes Remember the steps. Turn off all independent sources except one. Find the current or voltage due to that source. So we just felt have found the voltage due to the source. Now we're going to find the voltage due to this source. All right, so that's we're on Step three now repeats one and two for independent sources. All right, so we know that a voltage source becomes closed circuit and you know that a current source becomes open circuit. So if we would redraw this, it would look something like this. All right, so we just turned off this current source on this year is the node were working at This is where V X is All right, so once again, we just do, um, que CEO at that node. So that's in is equal to art we can divine defined the direction. So here it's going out. Yes, going out. And here it's going in. So in we have 0.2 v x Over here and out we have the X well cause V X two. All right, um, the X two that the same as a six to minus 00 at the ground over five. Then here we have the X two minus 11 because now it's not minus zero because it's a voltage store. So it's minus 11 divided by 10 then the X two is then equal to 11 volts. So the fourth step in the process to solve a problem using superposition is add the results together. So no, that means Vieques is equal to V X one plus v x two. You know that 60 volts plus 11 volts that is equal to 71 votes on that is your answer 23. Source Transformation + Example: in this video, I'll be giving guys some tips and tricks for source transformation. So, basically, um, if you have a voltage source and a resistor, you can convert it from Siri's two parallel, um on. Then you replace the voltage source with a current source. All right, and then, obviously, just convert using terms law to the required current or voltage. So you can either convert from a voltage source in Siris with the resistor to a current source in parallel or vice versa, and converted backwards. All right, why do you use force transformation? It's basically used to simplify a circuit in order to solve a problem much quicker and easier, then using another method. All right, so just some tips. When you transform from the one to the other, the arrow off the current source must be directed towards the positive terminal off the voltage source. So you see, it's plus minus with a plus at the top, so it the arrow is upwards. If this plus and the minus was the other way around, the in this area would face downwards. All right, um, you can also do it with dependent sources. So basically, source transformation isn't limited to independent sources. You could also use it for dependent sources. This is a very important point. I'll evil even label this nb Andi, do not transform the part of the circuits where the unknown variable is all right, so you'll have a large circuits and then there'll be a part of the circuit. Um, where the unknown variable is, for example, a voltage or current. So don't transform that part cuisine. You won't be able to figure out the voltage or current at that point. Then you can use any technique such as notable analysis mation. Alice is current or voltage division etcetera to solve these problems. So you just need to figure out the most appropriate technique in order to solve the problem using source transformation so we can do an example This question asks us to find are using source transformation. So now I Is this current over here going through this branch over here? All right, so we know this part must not be transformed, all right, cause this is where the unknown variable is. So, um, with this module, you can solve problems in many ways. For example, you could solve this problem you could label that note V one and that note view to and then you can solve for V one and V two and then you can solve for I using the one. But that's a lot more complicated and time consuming. So in order to solve this problem using source transformation, we can just transform these sources. And then all the elements will be in Siris because from current source you can convert a voltage source which will be in Siris. All right, so this would then become plus minus because remember, the direction of the plus must be at the are ahead. We have the 7.5 ohm resistor in this. The value of this is equal to 3.5 ampere 3.5 multiplied by 7.5 homes. And that would give you an answer off 26.25 volts. All right, moving on to do a trunk source transformation for this resistor on this current source, we'll get the following. We'll have the 12.2 and resistor, then this gets converted to a voltage source all rights on and he converted six. Remember, voltage is equal to current times resistance So it's six. I multiplied by 12.2 homes and that is equal to 73 0.2. I vaults right, because remember, this is a dependent voltage source. So that's why we haven't either. We have a ground, and then we have our six own resistor on the current flowing in this direction. So now all the elements joints Siri's, so we can then do Que vio que vio or rights. So we moving in a anti clockwise direction. So passive sign convention states. That's positive. Negative, Positive, negative, positive, Negative. So now all you do is the following plus six I minus 73.2 I plus 12.2. All right, Right, Cruz, we This represents a voltage is just on que vio and then we carry on plus 7.5 I Plus Now we're entering at the positive terminal 26.25 and that is all equal to zero. Um, notice how this value was negative because we inside at the negative terminal. If you solve this equation will get eyes equal to a value off 0.55 on piers on. That is your answer 24. Thevenins Theorem: in this video, I will be discussing some tips and tricks for seven INS. The're, um, Andi approach to hard to solve these problems. I'll give you guys a nice forced, a procedure for hard to calculate, orthe evident and a two step procedure to calculate feet seven. So, firstly, what is the evidence theory? It is when a linear to terminal circuit can be replaced by a voltage source, V seven in and a resistor or Sievinen. All right, you'll notice that the seven and equivalent is the source transformation off the North End equivalent. When calculating orthe Evan in, you have to switch off all the independent voltage sources and all the independent current sources. So by switching them off, the effect of this is a closed circuit for independent voltage source and in open circuits for an independent current source. All right, you guys should know what a closed circuit an open circuit is. Onda how to draw that in the in a question, but we'll do an example in the following video. If you still unclear about that, this the circuit in the question given includes a dependent voltage source, oil and or a dependent current source. You do not switch these off. Those who remain the same well, they just stay. They It doesn't change anything. But if it does involve a dependent source, then you must know that he must replace Terminal A B with a test source. Now, a test scores can either be a one ampere independent current source or a one vote independent voltage source so you could use either, depending on the question. What will be easier for the method you want to use to solve the problem? But I usually like to use the one ampere current source. All right, So to cock it, you What you do is you calculate V zero eyes era based on the test source. All right, And then once you've calculated either V zero I zero, you can punch that into and you know itis is equal to one. M p. R. And V test is one vault. And then you just substitute the value that you calculated fable day and you're being cooked. Get the value off arth evident. Just a little tip. If you have a circuit that looks like this, I have two terminals A and B then the voltage at point A, which is over here, is equal to the voltage between a B, which is equal to V seven. In over here we have V seven, all right, and that the same as voltage A B onda Reason V is equal to the A B. That is because of the A. B is equal to the A minus. VB on the B is equal to zero because it is that the ground So therefore, the baby is evil TV A. So this is quite a useful little thing to know the voltage up. That note is usually the voltage a B, which is V seven in all right now for the the steps, the steps to calculate feet even and Arthur even in. So the four steps to calculate Arthur even in the first step is to deactivate all independent sources. So that is what I mentioned earlier, where you either make it a closed circuit or an open circuit, depending on the type off independent source. The second step is to place a test source between a B all right, and that is only if there are dependent sources or at all, so you can just go and find north even in from there you can dangle calculate V zero Isar, whatever the unknown is. And then you can use only law to calculate or seven. So step three is calculating V zero eyes era on the instep. Four years, ERM stroll to calculate Ortho even in that is owns law over here to cock it or thinner. The two step procedure to calculate V seven in the first step is to define Vaeth Evan. So that is someone to what we were doing will be here. You need to define Vaeth evidence. So here we know that the voltage at note A is equal to V seven in Onda by being and by being able to solve for V A, you will be able to solve for wheat evidence because they are equal. So that's what the step here means. Defined the evidence then the second step is to find the heaven and using first principles . So basically, using the method that you find most appropriate whether it's nodal analysis or mission analysis or source transformation or anything like that, whatever you find most appropriate and then you can solve on find V seven. All right, In the next video, we will be doing a nice example which will cover most off the concepts that you need a known that you need to know for Lebanon. Fourth evidence there, um 25. Thevenins Theorem Example (Part 1): in this video, I will be doing the following example. The question states find V seven in on Ortho even in between points a B. So there's point a and there's point B, so we'll start off by calculating Arthur even in. All right on to do this, we follow this basic forced their procedure, as described in the previous video. So the first step to calculate Arthur even in is the activate all independent sources. Now we know that the independent sources off the ones shaped as a circle all right, Andi or independent voltage sources become a closed circuit, and all independent current sources become an open circuit. So if I were to redraw this, it would look like this. All right, so here we had the voltage source. It became a closer good. We had the current source. It became an open circuit. So it's like there's nothing even there because there's no current flowing. All right, so first thing you'll notice is that I zero is flowing through this branch. All right, on. And if we look at this dependent voltage source, its dependence on eyes era Sinaga branches no longer there, we know that I zero is equal to zero. All right, so therefore, their 0.5 eyes era is equal to 0.5 multiplied by zero, which is equal to zero volts to this little source, but terribly drawn. But that's the voltage source. That growth source is equal to zero volts so we can look at the next step. Now, step two is place a test source between a B. So we can choose to either put a test current source or a test voltage source. I like to usually use the test on current source. So do that. All right. And it's facing upwards on That's one and piers All right. So step three then tells us to calculate these era or Isar. So since we have the I, we want to calculate the V. That would be the voltage. At this point here, I'll just call this V T. All right. So, to calculate VT, you can just do nodal analysis. So that's, um, at VT in is equal to art to define the direction off current flow this is going in on. This is going out and this is going out. All right, so in we have one ampere and but we have VT. Here we have the ground. It's a VT minus. Zahra, over 30 owns, plus fut minus. You would usually say 0.5 eyes era. But since you know, 0.5 hours there is equal to zero volts, and you can just say Zira, divided by 20 plus 60 volts. Sorry, Paula. 60 owns. All right, So, um, if you solve for VT, as you can see, it's the only unknown on the 20 equation. So pretty is then equal to 21.82 volts. All right, so step full on. Called late art, even in is used earns law to calculate our seven. So here we have used the following over here, we used a current test source. So using this side so I test is equal to one appear on Visa or VT has been calculated. So, Arthur, even in does it equal to VT divided by I noticed E t is 21.82 Bolt on itis is equal to one ampere. That will give you a final answer off 21.82 homes. So that is your value for our thin Vernon. All right, So, in order to calculate, um v seven in, that will be done in the following video 26. Thevenins Theorem Example (Part 2): this'll is a continuation off the previous video where we just calculated Arth evident now to calculate Vita even in for this example before the following two step procedure. Firstly, we define the seven. So we know over here v seven in is the voltage between a. B writes um so we can write that off as you seven in is equal to voltage between a be all right on V A B is equal to a voltage in a minus the voltage at B But we know the voltage at B is equal to zero because it's at the ground. So therefore that is equal to V A. All right, so Fethi Vernon is equal to V a. So the voltage at this point v a is the same as the voltage at this note v a All right, so that's what we ultimately trying to calculate. And then that will be the value of V seven. So our first, like Teoh, find the direction or control we can I agree that you would use nodal analysis at the snowed. Um I will assume that current goes out this way. Here we have the current source, so we know it goes art. And we'll just assume goes art this way. All right, so by doing okay, CEO, that's node v A. We do the in close to art in. We have nothing. So that is just There are adults, Sarah amperes, right? And aren't we have 500 years plus out. We have the a minus 100 volts divided by 50 homes. All right, on Dhere. We also have it going art plus minus. And then you have the voltage tours, so it's minus 0.5. I zero on, then. We also have a voltage over here, so we'll just call this point the X. All right, then it would be minus Fi X, divided by 20 owns. All right, so if we just simply fire down this equation, we substitute I zero over here with five and piers. That's because if you look at the question, I zero is the current flowing through this branch, and that is the five MPs given by the current source. So by simplifying this equation, we get the following five p a minus three V X is equal to minus 92. Comma five. We're right. So now we have two unknowns on one equation. So it's not enough to solve for unknowns. So we know we need to make another equation. So you look what can you do to make another equation? Well, we can do the same thing, Casey. All but at this node. So que CEO knowed fi X go in is equal to aren't so. It's just defined that flow of current in we have over here we have. We define that the current Fords flying this way previously so it's going in and we'll just assume it's going after the here. You can assume it's being any direction as long as you write it out correctly. All right, so going in, we have on the same thing as this value here because this is what we defined it as the current going art. So the same is the current grain in here. So that's the A minus 0.50 minus V X, divided by 20. All right, plus and then eyes there is also going in. But you know, eyes there is equal to five amperes. So plus five and that equals two. The eggs divide by 60 x over 60. All right, so If we simply fire this equation, it will, um, results in the following minus three. He a plus for the X is equal to 292 kind of five. All right, so now we have two equations on toe Unknowns, V A and V X. Um, we then can punch this into our calculator. Let me teach a nice way of hard to do this. I'm not sure if you guys know, but if you're doing so, I'll teach anywhere you kick on mode equation, which is number five or right. Then you select the first option. If you have two variables on the second option, if you have three, so we'll go with one. I mean, you just punching these values five equals minus three equals minus. I need to 0.5 equals, and then the other question minus three equals four equals 292.5 equals. Therefore, the first value would be equal to so V A is equal to 46.14 volts. Andi, the X is equal to 107 comments 73 volts. So we can then conclude Therefore, V Sievinen, which is equal to V A, is equal to 46.14 volts 27. Nortons Theorem + Example: Norton's theorem is a linear to terminal circuit. Um, so we have two terminals that can be replaced by a current source I in Andi resistor or seven in which is the same as our Norton. All right, so that they would represent or Norton And that is in wooden. So when you do in order their own problem on between the two terminals or the load, you make that a short circuit. We're right. So a northern equivalent is the same thing a Z, a source transformation off the seven and equivalent. So if you like, you could just learn how to do seven and equivalents and then you just use the falling formulas to convert from feminine into Norton, um, or right. So when calculating or Norton, which is the same as our Sievinen, a current source becomes open circuit and a voltage source becomes closed circuits. So if we do the following example, um, this example asks us to find our Norton on the Northern equivalents. I n with regards to our now, our in this case is the load. So this year is the load. All right, so we'll start off by finding our Norton so as we mentioned isn't in the notes. When you want to find our Norton, you make the current forces open circuits and voltage sources short or closed circuit. All right, so if we redraw the circuit, it would then look like this. Here. We have an open circuit, and here we have a closed circuit. We have point a point B, and this year is our equivalent, which is the same thing as our Norton. So I due to the fact that it's an open source circuit here, it's as if the this resisted this resistant and this resistor aren't even connected. So that's what the circuit looks like. So you have 10 OEMs here, 10 arms here on day, 10 homes here. So, um, our Norton is then equal to 10 parallel with tin plus 10. Because these time, parallel on once calculate that it would give you five. And then now five would be in Siris with this 10. So you add them, he left with 15 homes. All right, so that's our Norton on our Norton is the same thing as Arthur Evidence. That's that's all the same. All equal to 15. All right. Between now in order to calculate I in we then replace the load with a short circuit, as mentioned on the nerds. A short circuits between the load or the two terminals. When you want to calculate Norton. All right, for to do that, we can re draw the circuits. You can read all the circuits, Um, that 10. And that tin is in parallel the court to share the same two nodes along with that and that . So if you simplify, we know 10 parallel with 10 gives you five homes and five homes. Then between the load, we have a short circuit. We have, ah, 100 volts source over here. So this is 100 volts. Means the voltage at this mood is 100 volts. Then here we have the three MPs, current source just like that. All right. And then here we have the ground. So, um, to calculate I Norton, we can simply say we can use nodal analysis so we know it's 100 volt here. So I Norton is equal equal to 100 volts, minus zero votes divided by five owns plus 10 homes. So it's 100 divided by 15. Right. And that will give you a final answer off 6.67 on piers. All right, this is simply because off, um, current is equal to voltage. Over resistance on that is what this represents. 100 minus serra, Um, along this section off the circuit. All right. So that you have it in Norton is equal to 6.67 ampere on Ortho even in or Norton is equal to 59 p. M. If the question Austria's should calculate, um, the seven in we, then is the following formula V seven n is equal to i Norton multiplied by our Sievinen. All right, I know or think we know is equal to 6.67 MPs. Right. 6.67 appears multiplied by earth evidence, which is 15 homes. Um, if you plug it into a calculator, 6.67 multiplied by 15 gives you a value off 100 faults, and that is your value off the Devon 28. Maximum Power Transfer + Example: this video, I will explain maximum power transfer on our then do an example. So if an entire circuit is replaced with its dividend equivalent, except for the load the power delivered to the load or then be equal to the following formula so the power would be equal to and the current marked applied by the resistance off the load, Um, which is equal to V seven in divided by Arthur even in plus the resistance off the load, all squared, multiplied by the resistance off the load so you'll have a load resistance. Then you'll have orth of inner and V seven in, and you just substitute those. They're used into this equation to calculate the power delivered to the look. The note. If I were ever it passed to calculate the maximum power transfer, then that means that our O is equal to Arth evidence. So the resistance off the load is equal to the or a feminine. So in those tour equal, that is when maximum power transfer occurs and you use the falling formula V seven and squared, divided by four times orthe even in or on the voltage off the across the, um a load resistor squared, divided by Ortho even in right. So if we have the following example, it asks us to determine p max delivered to resist the are so we have freezes toe are over here. So in order to calculate P max, we require, um v seven Andi orthe even in in order to calculate p max. So who started off by calculating Ortho? Even in Andi, as mentioned in a previous video for seven. In calculations, you follow the falling four step procedure to calculate or a feminine. So the first step is to deactivate all independent sources. And then the second step is to place test scores between a. B. But this step is only relevant full dependent, voltage on door current sources. All right, so basically, it's just a one step procedure and then you calculate orthe evident for this scenario. So by making all the voltage independent sources closed circuit so that would become closed and that would become closed on by making that the independent current sources open circuits. You're results in the following um, circuit. All right, so that's become an open circuit. So there's nothing there. Then you have a close circuit over there. Onda close circuit on the left over there. All right. The next step is to simplify the circuits. So over here I just read through it. So it's more need. And as you'll notice five and two in Siris, so five and two can then be added together on, then in parallel with one. So I just rotated it to its side because you probably most used to doing seven and examples between two points on the side like that. So basically, we calculate or Sievinen So that's one in parallel with five plus two. All right, search 1/1 plus 1/7, and that gives you 8/7. Then you flip the answer to give puts forth even and at the top, and you'll get 7/8 homes. So that is the value off arthemon. Now, to calculate the value, uh, V seven in you would start by using superposition. So if we have the following circuits, we could use superposition um, at this part of the circuits two converted to a voltage source. So here we have vehicles are times I so it's two homes multiplied by 16 amperes. All right, and then we would then calculate V seven in across these two points. All right, because he went to Novi Seven and across Resistant ar. So in order to calculate V seven in, we can do Casey. Oh, I'm sorry. Nor Casey a lot. We can do Cavey all So the seven in okay, we can define a current first for the Kay VL. We'll call this I so current flows from positive to negative. So flying this way. So you have the positive terminal here and the negative terminal beer. If we during que vio If we start here, we'll get minus five plus five I plus one I minus full plus two I minus 32 equals era. So if you simplify that, that will give you a value of I is equal to seven. Commerce six, um, to five appears seven commerce 6 to 5 on pier. All right, Eso no to calculate v seven in. We can work within this loop over here. All right, so if we have it a loop here and it's still I that's flowing within that group. Um we do que vio again. Andi, It will be plus one. I minus full it's entering at the negative, minus the thin in equals zero. If you simplify this the Sievinen but then be equal to three comma 6 to 5. Um, so you just substitute this. I've I've you into this. I andi you soulful V seven in all right, So we can now calculate the power, the maximum power transfer So P max is equal. TV seven and squared, divided by full, are given in V seven and squared is three comments. 6 to 5 squared, divided by four multiplied by on Ortho Vernon was calculated to be 7/8 rooms. All right, 7/8. And then that would give you a final answer off 3.75 watts. 29. Operational Amplifiers: Hey, guys, in this video, I'll discuss the theory behind operational amplifiers. Also called up temps on. I'll then give you some tips and tricks for hard to go about doing these questions in tests . So what is in our Pam? It is, Ah, high gain Elektronik Voltage amplifier. Now there are few ideal conditions that you need to know. I'll just discussed the most used ideal conditions. Um, so this is what an up and looks like. It's a little triangle with negative at the top and positive at the bottom. And these are two lead wise connecting to the open. No, the I one I two also called I negative and I positive always equal to zero under ideal conditions. Right on. Then the negative and the positive are always equal, and that's under ideal conditions. So this used quite a lot when you're doing problems. All right, the five standard open configurations you get the inverting, non inverting, buffer summing difference and then a non standard configuration, basically the most likely to ask a non standard configuration which will be something like a combination off the other five standard open configurations, and then you need to work with them together in order to solve for the unknowns. So the first, um, standard configuration is the inverting amplifier. You need to be able to identify what an inverting amplifier looks like by looking at the position off the resistance around the up ramp on the position off the voltage input. All right, so you need to know this formula V zero, which is over here, is equal to or to divide about or one multiplied by the input voltage. I'm not. If you don't memorize this formula, you could just do case yellow around the snowed Andi. The same applies to all the other, um, or the other op amps configurations. But I already did the Casey off all of them to result in the visa of formula. So you could just memorize all these formulas and it'll save you time in the test so you don't have to go and do Casey Oh, around each note along the time. All right, this is the non inverting amplifier. It's same as the inverting. Accept the position off the input. Voltage is now at the positive terminal over here on a visa is now equal to one plus or two of our one multiplied by V in. So they're the same. He just add that one plus All right, then you get a buffer amplifier, the most simple one, which basically states that the inn is equal to the art on. That's because off the ideal condition, if you remember, over here, um, the negative is equal to be positive. So the positive over here, which is V in, is equal to be negative, which is equal to VI zero. So therefore, Vienne is equal to the art. All right. The fourth standard configuration is the summing amplifier. Um, you need to know this formula v zero. Where are F in the numerator refers to the resistance off this resist Over here v one, V two and V three. Refer to these three vulture voltages over here on the three resistances. Refer to these three resistors over here, or rights. So don't get confused if, like there's not three resistance in parallel, Maybe the question might only have to off them. Then you would just like it's if there's any reason still wanted resistor to. And it looked like that then you know the formula just looks like that all right. And the same applies if there's more resistance than you just continue adding another one of these within the bracket, depending on harmony. Resistance, they are. So that's a summing amplifier. Then you get a difference. Amplifier. All right To calculate visa era. It's this long formula. Um, could seem a bit complicated to try. Memorize if you want to do Casey. Oh, you just in case you all that these two knows, and then you just substitute the one equation into the other and you'll be left with this formula. Yeah, Like I said, I'd recommend you just memorize the formulas. So it'll save your time in the test doing kcr. All right, um, so you must just memorize all of these, um, one of these different standard configurations. And you must know the positions off all the resisters on voltage sources. So you know what? Type off. Um, what type off standard configuration it is. So in the next video, I'll be doing a example. I'll do a simple example in the next video and the falling one, I'll do a little more complicated. One using a non standard configuration. All right. I hope this helps 30. Operational Amplifier Example: guys in this video, we'll be doing an op AMP. Example. All right. As you can see, there's an R pump over here. First step when you get an open question is you need to try identify which standard configuration is being used. So in the previous video, I showed you all the standard configurations. Um, on if you look at this example, there's a resist of a they they and their with two input for teachers. And this most closely resembles the difference amplifier, as you can see over here. So the question asks us to find these era. So here's the formula to find these era. Like I said, you just need to memorize this so you don't have to go and do case yellow at thes two nodes . Um, which will take up time during the test. So, um, just don't be deceived here in the question or one is the same as our one over here. But then there are two is our or three. So that might cause cause confusion when entering into a formula. So rather just focus on the positions of the resisters rather than what they call it. So are when he is 500 homes on our to his three killer arms. All right, so now we can look at this formula, um, which you should have memorized before the test. So V. Zahra is equal to are to are one if you just keep this diagram in the picture here, all right, so are, too. Which is this resistant? Divided by R one, which is this resistor said one killer own 1000 homes divided by 500 arms. Then we have two brackets at the top and the bottom. It's one plus one plus right or one over R two. So it's that resistor over that resistance. So it's this one over that one. So it's 500 over 1000 on, then at the bottom, we have our three of our full. So it's that resistance over that resistor. So three killer homes, 3000 over 6000 multiplied by V. Two multiplied by and V two over there and over there is equal to minus two million volts. So what, minus two times 10 to the negative three. Just keeping it involved so we don't get confused with units right then minus. There's not minus or two of our one or two throughout about or one multiplied by the one. So let's do that. Minus are to for the R one multiplied by V. One minus four times 10 to the negative three. Sorry, I just ran out of space there. All right. And then you punch that into a calculator, I'll just punch it in here quickly. So we have 1000 one plus 500 of 1000 divided by 500 one plus 3000 over 6000 multiplied by minus two times 10 to the negative three. Minus 1500. Multiplied by minus, four times sent to the negative three. All right on that gives you an answer off four times 10 to the negative. Three is equal to four times 10 to the negative. Three votes. Andi know the time sent to the negative three means Millie. So that for Milly Volts on. There's your answer. 31. Capacitors and Inductors: in this video, I'll be discussing capacities and in doctors. I'll be discussing the formulas you need to know on how to answer questions within doctors and capacities. All right, so firstly, I'll discuss the capacities and all the formulas. And after that, I'll do the in doctors and all the formulas. All right, so that is the symbol used for a capacitor. It's just two parallel lines connected to the two wires. The unit for capacitance is Farid, Um, that symbolized by capsule. If all right, they consist off to conducting plates separated by an insulator and die electric to calculate the voltage that is equal to one of the capacitance multiplied by the integral off current as a function of time. So the current as a function of time will be given. And then you integrate that between two points in time. Then you add the voltage at T zero. So the voltage will also be given as a function of time. The time zero you just substituted into there and you're calculate the voltage. He add all that together and should give you the voltage off the capacitor. All right. The in the currents is calculated as eyes equal to see multiplied by the derivative or voltage as a function of time. Energy is calculated as half the capacitance multiplied by the voltage squared, which is equal to the charge squared, divided by two times the capacitance a Z can see here. I've noted that the Charge Q is equal to see multiplied by V, so the capacitance multiplied by the voltage to calculate the power we all know powers equally voltage times current and that is also equal to capacitance. Multiply by voltage multiplied by the derivative or voltage as a function of time. Capacitors that are in Siris are treated as resistance in parallel. So you calculated like this one of the capacity of one plus one of the capacitance of two, plus one of the capacitance of three bottle of law. And then you add them all together, flipper over so you can calculate sea turtle, and that will give you the total capacitance in Siris. Andi capacitors in parallel. Ah, obviously the opposite This. So you treat them like they are resistance in Siris. So you just add them. C one plus C two plus C three, Um, now for the doctors and doctors, um, used this symbol over here. Um, it's like 12 little wire. All right, on the unit for that is Henry with a capital H, and doctors store energy in its magnetic field. So that's what doctors do. Then, to calculate the voltage, it's equal to induct INTs multiplied by the derivative off the current as a function of time. The current is equal to one over the induct INTs multiplied by the integral of the voltage between two points in time t zero starting time t ending time plus the function off current at time zero. So you substitute this time of year. Wherever there's a T in this formula on that will give you the current. All right, you add these two together and that will give you the the current through the doctor foreign doctors. All right, energy is equal to half the induct INTs multiplied by the current squared as mentioned earlier. These aren't functions of time. These are just value. Oh, off the doctor that the inductions off the doctor and the currents off the and Dr All right . The power through the doctor is equal to voltage times current, which is equal to the doctor is multiplied by the derivative of current as a function of time multiplied by the current right, So you know you'll notice, like everything between capacitance and inducts the opposite. So he has to see hips for capacitance. Here is inducted its carrots voltage or its current hits the derivative of voltage of the time, the voltage as a function of time. And here's a derivative off current as a function of time on that, like applies to all the formulas, basically just the opposite to each other in terms of voltage and, um, currents, right and doctors in Siris are treated like resistance in Siris off one plus all two plus off. Three on. The conductors in parallel are treated like resistance in parallel with one of the L one plus one of all two plus one of all three. You add them all together, you flip the final answer, and that will give you all turtle swap. Those are all right. In the next video, we'll be doing a simple example with capacities and in doctors 32. Capacitor and Inductors Example: Hey, guys, in this video, I'll be doing an example with capacitors and in doctors before a starter just like to mention that. If a question, um, says you must assume direct current conditions, then the capacitor becomes an open circuit. So it will look like that wherever the capacitor wars, it will be like there's nothing in between there. Andi Foreign in Dr It becomes a closed circuit. So it just connect with a wire in the position off the doctor. All right, so this is the example. It asks us to assume direct current conditions and find the total energy stored in the doctors and capacities. So here we have three capacitors, and here we have two in doctors to resisters on a current source. So, um, looking at water asks us, it's we need to know the direct current conditions, which is what I just mentioned to you guys. Now then we need to know the formulas to calculate the energy stored in capacities and in doctors. So the capacitor we use this formula for the energy don't be deceived by this w That just means work and work and energy that both measured in jewels are artists like same thing and in doctors we have. I'm this formula over here to calculate the energy. All right, so it's thought by writing out those formulas, First formula is the energy in the doctor that is equal to 1/2 multiplied by the inducted, its multiplied by the current squid in the energy for the capacitor is equal to one over, to multiply by the capacitance multiplied by the voltage squid. All right, so, like the question said, assume direct current conditions so we can just redraw the circuits in direct current conditions. Just so we have something to work from, because if you just like try, visualize this in direct current conditions, it's much easier to make a mistake. So induct has become closed circuit right on. Capacitors become open circuit. All right, so it's like there's nothing even in between this. All right, here we have the five killer arms, and here we have the 13 killer arms. All right, so just something to note is that the current over here is the current that flows through. Whether in doctors would be on the voltage over here is the potential difference between way. The capacitors would be, which would be over here. I'll just label this a B just for explanation. Purposes. All right, so it's starting this. All right, So we'll start by calculating the currents through the in doctors, which would be here, so their current is equal to three million peers. All right, you know that because of this current source and current stays the same in serious. So that's why we get this three million piers. All right, the voltage or the potential difference the A B. So it's between these two points where the capacitors were is equal to the voltage across the 13 killer own resistor, right? Why is that? That is because a B V A B is parallel to the voltage off this resistor. Because these time parallel on, we know that voltage and Paranal stays the same. So we can then right v equal to current times resistance. The resistance through the 13 killer resistor it's 13 confirmed, alright multiplied by the current, which he knows three million piers and that equals 39 volts. All right, Okay. So I hope you guys see that? That's that's like that. Any tricky parts we knew, you know, that the voltage across this resisted here is parallel to this one. So they are equal. All right. Now we can calculate the total induct ins that is equal to one plus 41 Henry plus 400 equals five. Henry. All right, we know that because in doctors and Siri's right, you just add them like that with doctors in parallel. Use the reciprocal, then for the capacitors. We have three capacitors in parallel. You know, capacitors in parallel. We add them. Andi, the passages in Siris, we use their reciprocal so calculates sea turtle. That is simply one plus two plus three. That is all those. So that is equal to six Micro Farid. Okay, so now we have all the unknowns we have. I we have that's over here, which is I Then we have V A B, which is this fee that we have all total, Which is that all? And see tonsil, which is that C? All right, so now we can just put everything into the energy formulas. It's one of the two multiplied by the all total, which is five Henry multiplied by the currents which is three times 10 to the minus three visiting 1,000,000 ps are just converting Turn piers, and that will give your final answer off 7.5 many jewels. Right? Then you do the same thing for the capacitor off CV squid half multiplied by C total is equal to six. Micro 10 to the minus six micro ferrets multiplied by V. And the voltage is 59 volts. All right, and then that should give you want of 117 Micro Jules on There are your two answers. 33. Phasors + Example: in this video, I'll be discussing phases, and I'll be into an example. So phases can be represented as a signal by the amplitude and phase off a Sinus oId. So if we have a Sinus oId, this is the amplitude on. This is the face. All right, So the three ways to represent a phaser is rectangular, um, which is uses an imaginary part on the rial parts, and then J represents the square root off negative one. All right, then, polar form, which is represented by our, which is the amplitude off the Sinus oId and fire, which is the phase and then exponential, which is basically our to the multiplied by E to the power of to the power of plus or minus J five. And then that is equal to cause five plus or minus. J sign Phi. So this e refers to the exponential function under calculator that little e over there. All right, so if you have the following Sinus word, um on, do you want to convert from this signal as a function of time to a phaser? If you convert to rectangular, right, and then we use the rectangular formula. Our cause fire, which is the same as X and then r sine phi is the same as why So then are we know is the amplitude on 45 degrees is fire, so substitute to seven cause 45 plus J multiplied by seven and multiplied by sine 45. And then that will give you a final answer off 4.95 plus 4.95 j To get it into polar form, you just take the amplitude and then angle buffets 45 degrees. So that one's a lot easier. And then exponential. Um, it's just our times e to the power off plus minus J five. So it's seven e to the power off because fires positive 45 it's positive J 45. All right, so just a way. How you would represent this on a graph? Over here we have the imaginary axis, all right, with positive jays all the way up here and negative jays down here and then along the x axis, we have the real axis. So if we wanted to plot this zero value here, then on the rial access, we have 4.95 which is the real part off the rectangular, um, representation. So it's 4.95 and then we have 4.95 j on its positive. So it's up here. Then you draw the line from zero to that point, and then the angle between, um that would be the face, which is 45 degrees, 45 degrees. All right, so the length represents the amplitude, which is seven. So are 67 in the angle from the x axis is the face 45 degrees. All right, Andi, note. You can only, um, do this plotted like this. If you working from a cause Sinus oId, it must not be signed. You must first converted to cause using trigger metric identities. Um, yeah, uh, identities. So you can just pause that and memorize all these. You have to know these identities. That's very important. Um, use it quite a lot for this section of work. All right, now we have fazer or athletic. Now, don't worry that this Faiza arithmetic may seem like a lot of formulas that you have to memorize because I know an easy way that you guys can do it on your calculator. So I'll do that in the next video 34. Phasor Arithmetic on Calculator + Example: in this video, I'll give you guys some tips and tricks to answering phase or thematic questions. So for any addition, operation or subtraction or multiplication or division, you can use your calculator on in complex mode. Mode number two. All right. And then you can just use this I value on this fazer angle, um, to answer the questions. Right. But if the question they give you has a square root, um, you might struggle to answer it because it will always give you a math era, for example, screwed off, uh, 60 angle 30 degrees equals. And that will give you a math era. So the Route one Is there anyone you need to memorize? So all you do is you take the amplitude or the are and you root that and then you divide the phase angle by two, right on the conjugate. It's also something that would be simple to memorize. Um, wherever there's a J in a congregate, you just make that negative. All right, So if it's a really negative and you just make it positive, and then that's how you do a conjugal it, let's do an example. You have the falling question determine I want in polar and rectangular form. The first thing you might try do is plug it into a calculator, but it'll give you a math era because off the square root so you have to do that, or Flynt or not on the calculator, so that would equal to the square root of 20 phase angle 40 divided by two minus five and then the Kontic. It makes this and negative J five, so this is the same as squared off 20 years, equal to full 0.47 All right, 4.47 angle 20 degrees over minus five, minus J five. So we can now plug that into the calculator. 4.47 phase angle 20 minus five minus J. Five equals on. Then there's your answer. 0.63 angle 1 55 degrees, and that appears so. It also asks us for rectangular form. So to do this the quick way you just click shift the number two and then you wanted in a plus B I, which is rectangular form. So you click number four equals, and then that is equal to minus 0.57 plus 0.2 seven j on piers, and that is your two final answers 35. Complex Numbers on the Calculator + Examples: Hey guys. So I don't know which calculator your own, but I would highly recommend. But you buy this Casio calculator if you own this one. Still a good calculator. But this one offers so much more. So basically, on this calculator you can solve simultaneous equations, matrices, whether it's two by 23 by three, as well as do all complex calculations for phase or athletic. Andi, that can't be done on this calculator. If you see here the options that gives you here, you can only have three options. Comstat and table, you have comp complex, that base equation matrix table Victor. So it's a lot more versatile Teoh to use this calculator. So let me show you what you would need to memorize if you don't own this calculator. All right? You don't know. Calculated. You're going to have to memorized all this phase arithmetic for, um, complex numbers. So if we have this in rectangular or in polar form, um, then you have to memorize all the ways for addition subtraction, multiplication on division. All right, as well as BP. How to calculate the roots, the inverse on the conjugal. It's all right. So now this can all be done using this. Casio defects 99 1 e s plus the silver one. All right. So you would also have to memorize a section called Transformation. And our transformation is when you converting from rectangular form to polar. So it's it's still basic to do this, but I'll just explain it anyway. R is equal to the square root off X squared plus y squared and then fire. This angle here is equal to the inverse of town over Why X And then you get that in verse of turn by going shift off turn and then you get 10 to the minus one, and then you can put the values over. Why an X there rights to calculate your angle. All right, so no, it's doing example. And I'll show you how you can use your court later to solve these problems. All right, so here at Oscar's devaluate the following and give the answer in polar form so that our angle fire our rights. Let me just extend the question Onda se andi um, in the form X plus j. Why? So that's rectangular form. All right, so if we have question one over here. All you do is punch. Put your phone into, um, put your sorry, not your phone, your calculator into complex mode. So to do that, you could click on mode over here, and then you click on number two and now you'll see over there it will tell your calculators and complex mode. So now you you punch this in. I said, open brackets four plus J for plus. And then on the calculator, it's eye for the imaginary square to minus one. So you just click that button I, which is enjoying it. Her adds close brackets, open records minus one minus two. I close brackets minus four, and then this angle is shift. Then you kick this little button here with a minus sign. You'll notice it as a little angle symbol over there like that. And then 60 degrees 60. All right, then, and just click equals. And then there is your answer. The answer is 13.9 angle minus 10. So now if you want to get this in rectangular format, you just click. Um, mode complex, um, mode. So a shift complex, right. And then you want the answer to be given in a plus. B I All right, So you click number four. He just rewrite that 15 points there. Nine angle minus 10 equals on. Then there's your answer. Beyonce would be 12.89 minus 2.27 j. All right, so now let's do the second example. Example Number two. Same thing. You just plug it. Orleans your calculator? Um, 10 plus four. I plus two. Angle City over minus to plus one. I plus eight angle 40 plus for I. All right, you quote might take a while to process, but there it is. Five calmer 38 angle. 63 0.8 degrees. All right. And the inter convert to rectangular with shift complex on. Then there we have rectangular we wanted calculate the conjugated you press number two. The arguments number one and polar number three. But we want to convert to, um Rectangular. So you click on four equals and then they have a two comma 44 plus four. Common seven. It's actually 80 j. Andi, There you have both your answers. I hope this hopes on, and I would really recommend you invest in one of these calculators because doing it manually in the test could take very long. And it's, um, you arm or going to make a mistake if you calculate it all manually. 36. Impedance and Admitance: Hey guys, in this video, I'll be explaining impedance and admitted admittance. All right, on the formulas you use now give you guys some tips and tricks for hard to approach these questions in tests all right, there. Example for impedance will be done in the following video. So impedance is the ratio or face a voltage V two phase a current I measured in homes, so you'll notice that sounds very similar to resistance. So here we have zero equals of the over I I'm so instead of on our for resistance, we have zid for impedance, but they're still both measured in terms. Admittance is the reciprocal of impedance measured in Seaman's That's a capital s for its unit. And then the symbol is why So why is it called one of his it so it's one of impedance. So that's the same as I over V. Over here is the national summarised table that you guys need to memorize. So the impedance for resistor is the same said is equal to our and admittance is one of our Whereas foreign doctors and capacities, you use the following to calculate impedance um J, which represents the square to minus one. Um W which represents the angular frequency. Alright, so that's the W over there. And then we have our which is the induct INTs and see, which is the capacitance. Um, So if the question told you to assume direct current conditions, you already know that you making in Dr Closed circuits on a capacitor open circuits and then if they say, assume high frequency conditions, then the in dr becomes open circuit and the capacitor becomes close circuits. So if we have a little impedance example over here, we the total impedance through this wire would be the resistance off the resistor R plus J Excel with excellence. W oh, so that's just J W, which will notice is the same thing as the impedance off on in doctor or right JW. So you treat them. You treat impedance like resistance and you just add them in Siris or the reciprocal for parallel. All right, so this is just another little example. If you have a capacitor, then its are for the resistance, plus one of the J, W C and J one of the J. W. C. Represents the impedance off a capacity. All right, so There's just one more thing you guys need to know for. The section is admittance all rights, and that one over said, which is equal to G, which is defined as conduct INTs and be that this defined as suspensions. Um, so that's just good to know, in case they ask it like that. If they tell you the conduct ins's and then you don't know what conduct since refers to, you know, it's, um, the rial part off this complex number. All right, then, over here, we just have the formulas to convert rectangular to phaser. You use this quite a lot, but if you have one of these calculators 37. Impedance and Admitance Example: Hey, guys, in this video, we are going to do the following example. Um, using impedance so impedance is defined as voltage divided by current. All right, so it's question Ask us to find V one. So that's this voltage at the at the conductor on the current I t. Says the current as a function of time. And that's this current flowing through the circuit. The ISS is given as a sign. All right, so we know to calculate I that is equal to the voltage or the source divided by the total impedance or the total resistance. All right, So, like I said in the previous video, you treat impedance like resistance. So we have the impedance off this resistant impedance off this in doctor, and you add them because they're in Siris to get the total impedance. So let's start by doing that. The turtle is equal to, um, impedance off the resistor, plus the impedance off the in Dr So that is equal to three plus Andi. By looking at these formulas, we know that the impedance often in doctor is J. W. Or actually, that's actually a Greek Oh, but J. W O J W is equal to five t times five and all is equal to the inducted. Its 0.3 Henry. That will give you an answer off. Three plus 1.5 j. Andi, that's bones. All right, so now we have zero turtle. All right, Um and we need ves in order to calculate the current So v s is given in sign. So we have to convert that to cause in order to write it as a phaser or right so we can use the identities. Here we have the identities we could use Onda. We have a positive sign, and we want to convert it to a positive cause. So we need to add a plus 90. All right, so to do that, give us where we can't currently have es equals 10 sign five t plus 20. So we need a plus 90 insider in order to convert it so that five t plus 90 minus 90 plus 20 . So by adding and subtracting 90 it same thing rights, we can then convert that same 10 sign five t plus 90 and that becomes minus 70. So now we have a plus 90. You were looking for so we can do the transformation. So that's 10 cause five T minus 70. All right, um, so if you write this, really, we can write this like this V s is equal to 10 angle minus 70 degrees. So that's in polar format now as a phaser. All right, so now that we have both of these in phases, even though this one's rectangular on this wine is polar, we can still solved. So that is I is equal to ves over 30 years is 10 angle minus 70 degrees, divided by three plus 1.5 j. So do that. Put this in the calculator. 10 angle minus 70. Divided by three plus 1.5 j equals. All right, so that is, um, an answer of 2.98 angle minus 96 0.56 degrees. All right, it's ah, we can now continue. That is our value for I t. Um, So, since it actually wanted it as a function of time, we could actually write it out like this. I t is equal to you. 2.98 cause five t. So that stays the same. Five t minus 96.56 degrees amperes. All right, so now we can calculate the one tee Savi One Is the voltage off this in, doctor? So in order to do that, we use the following equation. The doctor is equal to I times impedance at the in doctor. So we know the impedance at the conductor is equal to J W. Oh, all right, So we have i multiplied by J w O. And I is a current flowing through the in doctor. So we know that I current stays the same everywhere in Siris. So the current through the doctor is the same as this calculated value here. Well, here. So that is then equal to 2.98 angle minus 96.56 times J Times W is equal to the five five multiplied by Oh, just inducted in 0.3 7.3. Right? So you can once again just since our calculator. So that's what's your 0.98 angle minus 96? Come five six times. J times five times 0.3 equals 4.47 angle minus six. Come of 56 Once again, we can write V one t as a Sinus oId. So this is the amplitude 4.47 It's always cause w is still five t and then we have the phase angle minus six. Common 56 degrees on vaults. All right, I'm a lot of students. Often, once they're right at this entire Sinus story. Value difficult if you get two right votes or appears at the end, Um, and then you lose unnecessary marks. So I'm just creating awareness for you guys now, just so you don't make that mistake in a test, all right? 38. Leading and Lagging Sinusoids + Example: in this video, I'll describe easy method to determine leading and lagging Sinus or IDs. So the first step you'll be given V one and V two or I one and I to so that is the following here. Which Sinus weight is leading on by how much? Given V one and V two. The second step is to convert the signals to positive co sign. That's very important, positive co sign using trig identities. All right, so here we have a negative co sign which we knew convert deposit of coastline. And here we have a positive sign that when you convert a positive sign So we used the following trigger metric identities. All right, on the left hand side is what you'll have, and then the right inside is what it becomes. So, um, we currently have a negative cook cause only wants to be positive, cause So, um, what it becomes we could either choose this option minus cause over here minus cause here or minus cause here, all right, because when you multiply a negative and the negative, it becomes positive. All right. So we could use any I'm just going to use this one here So the plus 1 80 So we let then have V one is equal to minus 20 cause five T minus 10 plus 1 80 minus 1 80 All right, so, um, what we want to remain in order to be able to use the identity in this case will be the well, just leave the minus 1 80 behind, and then it will become a minus cost of beauty. So, yeah, we have that on day minus 1 80 So that's what remains behind. But what you do is you just simply fire it five t minus 1 80 So that's the identity in this year becomes plus 170. All right, so when we use this identity, it becomes minus minus cause which is positive. 20 because five t plus 1 70 And then you keep the 1 70 The 1 80 converted the cause to a positive. All right, now, to calculate V two, we have a positive sign that we want to become a positive cause. So the only thing here this would make it a negative cause of here. We wanted to become a positive cause, so we want the identity to have a plus 90. We're right. So we can start off writing it like this. 20 sign five T plus 90 minus 90 plus 100. All right, So, like I said, he wants the plus 90 to remain, because that's the identity over there. And then once he converted, it will become a positive cause or a positive 20. We re writer positive 20 cause five t and then you add the's too. Plus 10 degrees or right. So they we have are two signals converted to positive cut co sign. The third step is to transform the time signal to phase the form so that then this would then be the amplitude angle 1 70 degrees. And this one is 20 angle 10 degrees. All right, so there we have I'm the two Sinus oId in phaser format. All right, The fourth step is to draw the Sinus oId on the same Cartesian plane. So, um, if the phase angles positive, irritate this way, and if the phase angles negative, you rotate this way. All right. So let's just draw our Sinus Lloyds. So we have a Cartesian plane that looks like this V one has an angle of 170 degrees, so that would be just draw it in a different color over there. So that's V one, and then V two has an angle of 10 degrees. So that's over here. V two. So there's to sign the stories that have been drawn. The next step is to calculated acute angle between the two Sinus words. So, um, if this year is 10 degrees and this year is 1 70 it means this angle here is also 10 degrees, so they're cute. Angle between the two Sinus oId will be equal to 180 minus 10 minus 10 which will result in 160 degrees. So that's 160 degrees. So now the final step is to rotate the Sinus oId anti clockwise on the first Sinus way to reach zero degrees is leading. So if we have off to Sinus Lloyds like this Andi, over here we have the one. And here we have V two. If you rotate this anti clockwise right, the 1st 1 to touch zero degrees is V one, so that means V one is the leading Sinus oId so you can conclude by writing V one leads he to by and then you write the value of the acute angle 160 degrees, and that is your final answer. 39. Sinusoidal Source Transformation Example: the following question asks us to use source transformation to find I X Now I x is a current flowing through this, um capacitor right on I X is also value in this dependent current source over there. So the question sells us to use force transformation. Usually, when the question told you to use a specific method, you should, because that's usually the most easiest way to solve that specific problem. So we can convert. This can convert these two parts to voltage sources using source transformation. So that would look like this. But the positive is in the direction off the ahead when you do source transformation. Then we heard it in Siris. Now you forgot how to do source transformation. You can just go to recap on the video off source transformation, then have a capacitor on our are the vantage force Dr for us. So you can just write all the values. This is five homes, the impedance off. This is minus J four homes. Um, this voltage way no voltage is equal to resistance times current. So the resistance is in this case is impedance multiplied by current and the impedance is seven plus six J multiplied by the current, which is five angle is ever degrees. All right can plug them into the calculator. Seven plus six five times five, is there? Uh, that will give you the father and answer. Um, all right, so that's 13 comma 81 angle. 76 comma. 87 All right, so this is in vaults, then over here, we have the impedance off this in doctor, which is seven plus six j. Here we have. Once again, it's resistance multiplied by currents of the current. Is there a point to I multiplied by five? The resistance on that is equal to one i x so just x Wait. Don't transform the part off the circuits That way the variable is that we are trying to find, which is in this case, I X. All right, so now it's pretty basic to so far XP Just do. This is the direction of i X, and we can then do cave young. So moving up this way for getting minus X plus five x minus four J on X minus 30 angle 76 87 plus seven plus six j X. And that is all equal to zero. All right, so now if we highlight the part with the like terms we have extended on over there way just have constant value. So if we are, although I expect used together, it will give us the falling answer. So he's saying, minus one plus five minus four I plus seven plus six. Just double check that plus five minus four J plus seven plus six, right, and that gives you an answer off. 11 comma 18 angle. 10. Common 30 i X and then you can bring us over to the other side and make it a positive So that 30 angle 76 common 87 degrees We're on it, so then we can find I fix 30 Angle. 76 Common 87 degrees, divided by 11 Common 18 Angleton Common threes er degrees on. I give you the final answer off. Just double check that. All right, that be close. Two comments. 68 angle. 66 Common 57 degrees And that they will appears the question to in state whether they want the answer in, um, rectangular or perform. So just give the ants in both. So that's in polar and then rectangular quickly. The quick way to do it is on calculators. You just say Shift number two. All right, shift to click number four for rectangular form, then that gives you an answer. One comment. There. Seven plus two comma for six J. I'm Piers and they are your final answers. 40. Sinusoidal Thevenin Equivalent Example (Part 1): Hey, guys. So this example is usually, um, the lost type of question they ask in the test. So it's usually a feminine or north and question with complex numbers and in phases, form and all that, you know. So I'll do an example just you guys could know. Howdy. I'm go about doing one. So this question also is to find the equivalent impedance in rectangular form, So that's the same as equivalent resistance. But in this case, it's impedance because you're working with a complex numbers on, then find V seven and in polar form so and they'll start off by calculating, um, zero equivalent rots on. If you remember from the seven in on Northern Videos we have this forced the procedure to calculate Arthur even in in this case, it's 07 in Was it equivalent? So the first step is to deactivate all independent sources. That's the current source has become open circuits and voltage source has become closed circuit. But that's only for the independent sources. Right then you place a test was between a B, and this is only if you have an a dependent source somewhere in the circuit. In our case, we do, We have a dependent source. So we will be placing a test source. Third, calculate V zero or eyes era. In our case, that would be V A and then used owns law to calculate Arth evident. All right, so let's do that. So we have our circuits. So first we deactivate all the independent sources. So this becomes an open circuit, Andi. Then we left with lift with the following circuits. That's 14 arms. That's J V A. And this is minus two J urns. So second step is we added test source. I'm going to add a You can either at a voltage stores, um, or a current source. Um, I think in this case, it would be easier to add a, um, a voltage source or one ampere. But no, I'll just keep Teoh the way I like to usually solve it with a one ampere current source. So we have this note at the top on this note every year is V A. All right, so you can just do nodal analysis. It is equal to art. So here we have the screen in with humans. Green Carta on departure. So in we have one ampere. And we have one out. We have V A minus zero over which has a grant. It's minus zero, divided by the, um impedance minus two J right plus V A minus. J v a divided by 14 arms. All right, so now we need to calculate for the unknown V a. All right, So if we have a common denominator, that would be the common denominator would be equal to minus 14 j All right, so then if we multiply the numerator, um, we'll get minus 14. J equals here. We just need a multiplied by seven to get that denominated to my foot. And Jason's just seven p a. And then here we need to multiply by minus j So get minus. J p a. And then he will have minus j times minus. J rots and they didnt that'll give us plus one angle 1 80 Be a rock. So now we can add all these together cause the whole d A's. So we'll have seven minus j plus one angle 1 80 seven. I shapeless one, everyone 80 and that is equal to six comments there. Eight ankle minus nine. Comet, 46 degrees okay, minus 14 j. So now we can solve for V A se minus 14 j divided by this. So we have minus 14 j divided by the answer and therefore the A is equal to two comma 30 angle minus 80 comma five before degrees or aren't so. Now we used way do the fourth step, but the fourth step is used earns law to calculate arth evidence. So our Sievinen in our case is, um Zid seven in which is their equivalent is equal to, um the voltage divided by the resistance. So it's the a divided by I test, and the tests will be used one NPR. So it's just v a divided by one the a divided by one which will just be equal TV A So, therefore, is it equivalent is equal to verse vat value. But remember there also to find Zedd equivalent in rectangular form. So for that, we can do that on the calculator. Just click shift to number four equals And there you have the answer. It is 0.38 minus J to come in to seven bones. So there's your answer for is it equivalent? All right. In the next video, we will calculate the seven in in polar form for the same example 41. Sinusoidal Thevenin Equivalent Example (Part 2): Hey, guys. So in the previous video we just calculated are equipped for Z equivalent um, the equivalent impedance between points a B on Now we are going to find the heaven in in Pota for so finding veto. Even in we followed a two step procedure. The first step is defined v seven in on second step Step is fine Vaeth evident using first principles by first principles I just mean Notre analysis or mention Alice or whatever technique you want to use to solve the problem. So Step one is defining V seven in. So we know the feminine is over here between points a B So the A B is equal to v Sievinen. Andi Um, that the same as v a voltages a minus the voltage will be. And you know the voltage at B R Ground is equal to zero. So therefore, Vaeth even in is equal to V a. All right? And so we will look at this node over here. It's just high like this mood, right? And we'll call this note v A so we can use, um Nuttall. Analysis in is equal to art so we can just issue it's going aren't you? Um well, this unit screen Arte on this. Humans grand art here, even though most poorly going in p cause this current sources going arts, it needs something to go in. But we will just assume that it's going out. You'll still get the same answer for V A. As long as you right off the equations correctly. So in we have nothing. So that, Sarah equals are we have three angle zero degrees right out we have plus the A minus J the a divided by 14 homes, then plus V a minus zero divided by minus two j. All right, so I'm here. We can have another common denominator to try solve v A. So according common denominator will be, um, minus 14 j rights. So you have zero times minus 14 j, which will be equal to zero. All right, Is it your zero multiplied by minus 14 j zero in three. Angle zero is equal to three. So it's just three angles. Era multiplied by minus 14 j. No kids. 42 angle minus 90 degrees. Here we just knew multiplied by minus. Um seven j no, just by minus J. All right, so we'll get minus J V A on minus J times minus J is equal. Teoh plus one angle 1 80 e a. Plus here to get this to the common denominator Just multiplied by seven. So that's seven today. All right, so, no, we look at what we have. We have this year in terms of ea We have this in terms of the A in this. So we just want to simply fire this now. So again, you just use your calculator minus J plus one angle 1 80 plus seven. All right, then they don't give you an answer off. Six comments. 08 angle minus nine. Comment 46 He a All right, And then this You can bring over this four comma 42 angle minus 90 to the other side. So it's minus 42 angle minus 90 degrees. All right, so we're just trying to get V A on its own, so you'll have a mind of 42 angle minus 90 degrees divided by this value. Six colleges era it angle minus nine. Combat 46 equals P A. All right. So, um, if you punch this inter calculator, it will give you an error because you haven't negative our value. Let me just show you what I mean. Um, minus 42. Angle minus 90. Divided by six. Calmer. There are aides minus nine. Comet 46 All right. It gives you a math error, right? That is because the general for metal pole it is our angle fire rights. And then this fight can either be positive or negative. But this are always has to be positive that that is a rule that you need another. All rights are is always positive. And I'll show you hard to go about answering this. Basically, you just get rid of this negative right on. You'll get an answer. So v a we'll then be equal to six comma 91 angle, minus 80 kind of 54 degrees votes. All right, so that's the answer with a negative in front of it. Because we took her way than negative in the calculation. Right. But we know you can't have a negative. Are are always has to be positive. So if you were to draw this art, we have a radius off six Common 91 in length on at minus 80. Calmer. 54 degrees. So we know this year is minus 90 degrees. That Zahra degrees, That's 90. That's 1 18 Right, So then the value will be here. All right, so this is this angle here is minus 80. Common five four degrees. All right, Um, but this is when the R is negative. So this are here is six common 91 Um, so when it's negative, you just take it to the other side like this. She just continue straight line, all right? And then they must be the same link of radio. So that's six common 91 This is minus six. Common 91 This is our is equal to positive 69. And then this angle here is now equal 2180 minus eight. Some common 54 Right. So in this angle, here is 99 common for six degrees. So then our final answer for V A would be equal to six. Common 91 angle. 99 common. 46 degrees votes on. There you have it. That's your their youthful V's evidence. Because, you know, the A is equal to beat evidence on it. Wanted the answer in polar form on that is in polar form