Kirchhoff's voltage law | Circuit analysis | Electrical engineering | Khan Academy

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 Kof's laws. In this video, we're going to talk about Kof's voltage law.

If we look at this circuit here, this is a voltage source. Let's just say this is 10 volts, and we'll put a resistor connected to it. 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. 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 were 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 1 volt. A rise of minus 1; 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 write a little expression for this, which is: V rise minus V drop 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 Kirc hoff'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 just get is 10 minus 10 equals 0. I'm going to draw this circuit again. Let's draw another version of this circuit, and this time we'll have two resistors instead of one. We'll make it, uh, whoops, we'll make it two 100-ohm resistors, and let's go through and label these. This is again 10 volts, so this node is at Z volts.

This node is at 10 volts. What's this node? This node here is, these are equal resistors, so this is going to be at five volts. That's this node voltage here with respect to here, so that is five volts. This is 5 volts, and this is 10 volts. So let's just do our visit again. Let's start here and count the rises and drops.

Okay, we go up 10 volts, then we have a voltage drop of five, and 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 5 minus 5 equals 0.

All right, so I can generalize this. We can say this in 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 Kirc hoff'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 going to go up 10 volts, down 5 volts, and down 5 volts. So what we're adding is the voltage rises. We're adding all the voltage rises: rise + 10, that's a rise of minus 5 and a rise of minus 5.

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, Kirc hoff'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 5, minus 5, 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 5 rise, plus 5 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 Kirc hoff's voltage law.

We're going to pair this with the current law, Kirc hoff's current law, and with those two, that's our tools for doing circuit analysis.