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Anderson Video - Kirchoff's Loop Rule

Professor Anderson
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Okay, the second rule is called the loop rule, and the loop rule says the following: around a circuit loop, the voltages that are rising minus the voltages that are dropping has to equal zero. So these would be like your batteries. These would be your resistors. So any circuit, what it says is the voltage drops that you rise on, minus the ones that you drop on have to be zero. So let's start right here, and let's go around the circuit like this. The very first thing I do is I go through a battery, and so I rise. I get plus V. The next thing is I go through a resistor, and so that is a drop of IR. And that's it for this simple circuit. And so I get back to zero where I started from. And this is, of course, just Ohm's law, right? If I move IR over to the other side I get that. And we say we're happy. But let's say that we have more than one resistor in there. Let's see how this loop rule works. So let's do a simple battery again, but we're gonna add two resistors. R1 and R2. And there's some current I that's flowing in this circuit. So once again, let's start right there and we'll go around the circuit in that direction. So the first thing we do is we hit the battery. That's positive, we've gone from the negative terminal up in voltage to the positive terminal, so we have a plus V. And then we go through resistor R1 that's a voltage drop of IR 1. And then we go through R2, and so that's a voltage drop of IR 2. And all of that is equal to zero. And so we get back to what we already knew, if I put both those on the other side, I get IR 1 plus IR 2. Or, I times R 1 plus R 2. Or, I times R series. Now, in the problem that we were just looking at, they wanted to know the voltage across a 960 ohm resistor. So let's think about this for a second. Let's say that this is, up here we will call this V A, we will call this V B, and we will call this V C. And we'll draw everything relative to ground here. what can we say about V A? V A is just equal to the battery voltage, V. But V B, the voltage here, is going to be less than that. V B is going to be the battery voltage V, minus how much it drops through R 1. So that's gonna be a little bit less because you have current and you have resistance. V C is, of course, going to be zero. Right, you're already down here. Okay, so let's see if we can do our problem and attack part B.