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Kirchhoff's voltage law

Kirchhoff's Voltage Law says if you travel around any loop in a circuit, the voltages across the elements add up to zero. Created by Willy McAllister.

Video transcript

- [Voiceover] Now we're ready to start hooking up our components into circuits, and one of the two things that are going to be very useful to us are Kirchhoff's laws. In this video we're gonna talk about Kirchhoff's voltage law. If we look at this circuit here, this is a voltage source, let's just say this is 10 volts. We'll put a resistor connected to it and let's say the resistor is 200 ohms. Just for something to talk about. One of the things I can do here is I can label this with voltages on the different nodes. Here's one node down here. I'm going to arbitrarily call this zero volts. Then if I go through this voltage source, this node up here is going to be at 10 volts. 10 volts. So here's a little bit of jargon. We call this voltage here. The voltage goes up as we go through the voltage source, and that's called a voltage rise. Over on this side, if we are standing at this point in the circuit right here and we went from this node down to this node, like that, the voltage would go from 10 volts down to zero volts in this circuit, and that's called a voltage drop. That's just a little bit of slang, or jargon that we use to talk about changes in voltage. Now I can make an observation about this. If I look at this voltage rise here, it's 10 volts, and if I look at that voltage drop, the drop is 10 volts. I can say the drop is 10 volts, or I could say the rise on this side is minus 10 volts. A rise of minus 10. These two expressions mean exactly the same thing. It meant that the voltage went from 10 volts to zero volts, sort of going through this 200 ohm resistor. So I ran a little expression for this, which is, v-rise minus v-drop equals what? Equals zero. I went up 10 volts, back down 10 volts, I end up back at zero volts, and that's this right here. This is a form of Kirchhoff's voltage law. It says the voltage rises minus the voltage drops is equal to zero. So if we just plug our actual numbers in here what we get is 10 minus 10 equals zero. I'm gonna draw this circuit again. Let's draw another version of this circuit. This time we'll have two resistors instead of one. We'll make it... We'll make it two 100 ohm resistors. Let's go through and label these. This is again 10 volts. So this node is at zero volts. This node is at 10 volts. What's this node? This node here is... These are equal resistors, so this is gonna be at five volts. That's this node voltage here with respect to here. So that is five volts. This is five volts. And this is 10 volts. So let's just do our visit again. Let's start here and count the rises and drops. We go up 10 volts, then we have a voltage drop of five, then we have another voltage drop of five, and then we get back to zero. We can write the sum of the rises and the falls just like we did before. We can say 10 volts minus five minus five equals zero. Alright. So I can generalize this. We can say this is general we can do the summation, that's the summation symbol, of the v-rise minus the sum of the v-fall equals zero. This is a form of Kirchhoff's voltage law. The sum of the voltage rises minus the sum of the voltage falls is always equal to zero. There's a more compact way to write this that I like better, and that is, we start at this corner... We start at any corner of the circuit. Let's say we start here. We're gonna go up 10 volts, down five volts, and down five volts. So what we're adding is the voltage rises. We're adding all the voltage rises. Rise plus 10. That's a rise of minus five and a rise of minus five. So I can write this with just one summation symbol. The voltages around the loop, where i takes us all the way around the loop, equals zero. So this means I start any place on the circuit, go around in some direction, this way or this way, up, down, down, and I end up back at the same voltage I started at. So let's put a box around that too. This is Kvl, Kirchhoff's voltage law. Now I started over here in this corner, but I could start anywhere. If I started at the top and went around clockwise, if I started here say, I would go minus five, minus five, plus 10, and I'd get the same answer. I'd still get back to zero. If I start here and I go around the other way, the same thing happens. Plus five rise, plus five rise, and this is a 10 volt drop, so it works whichever way you go around the loop, and it works for whatever node you start at. That's the essence of Kirchhoff's voltage law. We're gonna pair this with the current law, Kirchhoff's current law, and with those two, that's our tools for doing circuit analysis.