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Read more. Subscribe via email. Labels: basic electronics pdf , EDC book pdf. OK, so by choosing I going in this way into the positive terminal, the power consumed by the element is going to be positive.
OK, so in general of even simply following this convention, when I label voltages and currents, I'll be labeling the current into an element entering in through the plus terminal. Remember, of course, if the current is going this way, let's have one amp of current flowing this way, then when I compute the current, "i" will come out to be negative.
OK, so by making these assumptions, the assumptions of the lumped matter discipline, I said I was able to simplify my life tremendously. And, in particular what it did was it allowed me to take Maxwell's equations, OK, and simplify them into a very simple algebraic form, which has both a voltage law and a current law that I call Kirchhoff's voltage law, and Kirchhoff's current law.
KVL simply states that if I have some circuit, and if I measured the voltages in any loop in the circuit, so if I look at the voltages in any loop, then the voltages in the loop would sum to zero. OK, so I measure voltages in the loop, and they will sum to zero. Similarly, for the current, if I take a node of a circuit, if I build the circuit, a node is a point in the circuit where multiple edges connect.
If I take a node, then the current coming into that node, the net current coming into a node is going to be zero. OK, so if I take any node of the circuit and sum up all the currents going into that node, they will all net sum to zero. So, notice what I've done is by this discipline, by this constraint I imposed on myself, I was able to make this incredible leap from Maxwell's equations to these really, really simple algebraic equations, KVL and KCL.
And I promise you, going forward to the rest of 6. It's actually really, really simple. It's all very simple algebra, OK? So, just to show you an example, let me do a little demonstration. Let me build let me build a small circuit and measure some voltages for you, and show you that the voltages, indeed, add up to zero. So, here's my little circuit. So, I'm going to show you a simple circuit that looks like this, and let's go ahead and measure some voltages and currents.
In terms of terminology to remember, this is called a loop. So if I start from the point C and I travel through the voltage source, come to the node A down through R1 and all the way down through R2 back to C, that's a loop.
Similarly, this point A is a node where resistor R1 the voltage source V0, and R4 are connected. OK, just make sure your terminology is correct. So, the circuits up there, could I have a volunteer? Any volunteer? Come on over.
OK, so let me take some measurements, and why don't you write down what I measure on the board? What I'll do is, let me borrow another piece of chalk here. What I'll do is focus on this loop here, and focus on this node and make some measurements.
OK, so the next one is It is The measurements, I guess, have been this way. OK, so within the bonds of experimental error, noticed that if I add up these three voltages, they nicely sum up to zero. OK, next let me focus on this node here. And at this node, let me go ahead and measure some currents. What I'll do now is change to an AC voltage so that I can go ahead and measure the current without breaking my circuit.
OK, this time around, you'll get to see the measurements that I'm taking as well. So, what I have here, I guess you can see it this way. What I have here is three wires that I have pulled out from D. And this is the node D, OK?
So, I have three wires coming into the node D just to make it a little bit easier for me to measure stuff. OK, so everybody keep your fingers crossed so I don't look like a fool here. I hope this works out. So, you roughly get, what's that, 10 mV. OK, so it's about 10 mV peak to peak out there, and let's say that if the waveform raises on the left-hand side, it's positive.
So, it's positive 10 mV. And this time, it's a negative, roughly 20, I guess, So, I'm getting, in terms of currents, I have a , , I'm sorry, positive 10, positive 10, and a that adds up to zero. But more interestingly, I can show you the same thing by holding this current measuring probe directly across the node.
And, notice that the net current that is entering into this node here is zero. OK, so that should just show you that KCL does indeed hold in practice, and it is not just a figment of our imaginations. So, before I go on, I wanted to point one other thing out. Notice that I've written down two assumptions of the lumped matter discipline, OK? There is a total assumption of the lump matter discipline, and that assumption is, in spirit, at least, shared by the point mass simplification in physics as well.
Can someone tell me what that assumption is? A total assumption, which I did not mention, which you can read in your notes in section 8. A total assumption to be made here is that in all the signals that we will study in this course, we've made the assumption that the signal speeds of interest, transition speeds, and so on, are much slower than the speed of light.
OK, that my signal transition speeds of interest are much slower than the speed of light. Remember, the laws of motion, the discrete laws of motion break down if your objects begin moving at the speed of light. OK, the same token here, our lump circuit abstraction breaks down if we approach the speed of light.
And there are follow on courses that talk about waveguides and other distributed analysis techniques that deal with signals that travel close to speeds of light. OK, so with that, let me go on to talking about method one of circuit analysis. So just based on those two simple algebraic relations, I can analyze very interesting and complicated circuits. The method goes as follows. So, let's say our goal is, given a circuit like this, our goal is to solve it. OK, in this course, we will do two kinds of things: analysis and synthesis.
Analysis says, given a circuit, OK, what can you tell me about the circuit? OK, so we'll solve existing circuits for all the voltages and currents, voltages across elements, and currents through those elements.
Synthesis says, given a function, I may ask you to go and build circuits. OK, so for analysis here, we can apply this method that I want to show you. And the idea here is that, given a circuit like this, let us figure out all the voltages and currents that are a function of the way these elements are connected. The first step is to write down the element VI relationships. OK, right down the element VI relationships for all the elements. That's it.
So, what we'll do, we'll do an example, of course. But, just as a refresher, we've looked at a bunch of elements so far, and for the resistor, the element relation says that V is pi R, where R is the resistance of the element here. For a voltage source, V is equal to V nought. That's the element relationship. And for a current source, the element is the relation is, "i" is simply the current flowing through the element.
OK, so these are some of the simple element rules for the devices that the current source, voltage source, and the resistor. OK, if you turn to page five of your notes, I'm going to go ahead and edit the circuit here. You can scribble the values on your notes on page five. So, before I do that, let me go ahead and label all the voltages and currents that are unknowns in the circuit. So, let me label the voltages and currents associated with the voltage source as here.
Notice, I continue to follow this convention where whenever I label voltages and currents for an element, I will show the current going into the positive terminal of the element variable, OK, after element variable voltage.
Let me pause here for five seconds and show you a point of confusion that happens sometimes. Often times, people confuse between what is called the variable that is associated with the element versus the element value. OK, notice that here, capital V nought is the voltage that this voltage source provides, while this name here, v nought, is simply a variable that we've used to label the voltage across that element. So, similarly, I can label v1 as the voltage across the resistor, and i1 is the current flowing through the resistor.
So this method of labeling, where I follow the convention, that the current flows into the positive terminal is called the associated variables discipline. I was trying to use the word discipline in situations where you have a choice, OK, and of a variety of possible choices, you pick one as the convention. OK, so here, as a convention, we use the associated variables discipline, and use that method to consistently label the unknown voltages and currents in our circuits. OK, so let me continue the labeling here, v4, i4, i3, v3 here, and v2 and i2, v5, and i5.
I think that's it. So, I've gone ahead and labeled all my unknowns. So each of these voltages and currents are the voltages and currents associated with each of the elements. And my goal is to solve for these. OK, so in terms of our solution here, let's follow the method that I outlined for you.
So, as the first step I am simply going to go ahead and write down all the element VI relationships. GreatST Newbie. Points 1 Location Faridabad Student of Engineering.
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