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## AP®︎/College Physics 1

### Course: AP®︎/College Physics 1>Unit 11

Lesson 4: Kirchhoff's loop rule

# 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.

## Want to join the conversation?

• Whenever he labels certain points as having voltage, I get confused. Isn't voltage measured between two points? Am I missing something here?
(29 votes)
• Hello Jason,

You are correct, voltage is measured between two points.

Often we take a shortcut and assign one lead to "ground." This is typically the low voltage point on the circuit e.g., the negative terminal of the battery.

Now we can say "The voltage is 9 VDC." This is easier than saying "The voltage is 9 VDC relative to the negative terminal of the battery."

Regards,

APD
(33 votes)
• Why is it that if the resistances are equal (100 ohm and 100 ohm) , the voltage gets halved to 5V?
(27 votes)
• Check out the article on the Voltage Divider where we derive the voltage at the junction between two series resistors. In the special case where the resistors are the same value, the voltage at the node where they are connected is exactly half of the total voltage across both of them.
(27 votes)
• Why is the bottom node at 0 volts?
(16 votes)
• Picking a node to be 0 volts is kind of like getting to select where 0 elevation is when you measure height. You have some discretion. If you are measuring the height of mountains the usual 0 elevation is sea level. When you measure your own height, zero height is usually the floor. With circuits, you get to select one of the nodes in the circuit as the reference node. In circuits with just a single power supply, the schematic is drawn such that the reference node is near the bottom of the page, and nodes with positive voltage are drawn higher up on the page.
(24 votes)
• What is the reason for this voltage drop?
(18 votes)
• Voltage is potential energy. It is stored inside a battery and has nowhere to go. Once there is a circuit the potential energy is released, and as the potential energy is releasing, it is lowering. Think of the battery as the top of a hill and the zero volts point the bottom.
Hope this helped!
(13 votes)
• I thought that voltage was just a change in potential difference and it was constant throughout a continuous circuit? So how can it be 10 V at one point of the circuit and 0 V at another? Am i missing something, because in the ohm's law videos sal wasretty clear that voltage is constant throughout a circuit.
(7 votes)
• Sal says the current is the same everywhere in a 1-loop circuit, not voltage.
(15 votes)
• How does the voltage get like "used up" but the charge is conserved?
I mean there's charges flowing at any point in a closed circuit but at certain points there isn't any voltage on the charges?
(4 votes)
• Voltage is a potential, it really doesn't have a value at a point. Voltage, like any potential, is always measured between two points, in a circuit it is usually measured between the point you are interested in and the negative or ground in the circuit.

Let me use gravity as an example of a similar process. You have a 1 kg rock that is 2 m off the ground, it is coincided to have 19.6 J of gravitational potential energy, if that same rock moved to 1 m off the ground it will have 9.8 J of gravitational potential energy. It no longer has the same potential energy but the mass is the same. This is the same as the voltage having decreased but the change stayed the same.
(15 votes)
• What does 0 Volts mean? Is it possible to have a circuit running with 0 Volts in one path as shown?
(10 votes)
• Potential difference is measured in volts. If there's no potential difference between two points, then they are at the same potential and no charge will move between those two points. to produce a potential difference a cell has to expend some of its chemical energy in it.
(2 votes)
• If a circuit contains ONLY power source(battery) connecting via wire from positive terminal to negative terminal, will it obey the KVL? There is no element that allows the voltage to drop when it reaches the second terminal.
(7 votes)
• There is an element: the wire. It might have very very low resistance, but it's not zero. There will be a lot of current! KVL will hold.
(3 votes)
• Is the voltage always 0 for the node that goes into the minus side of the voltage source?
(3 votes)
• Hello Erik,

No it is not. Case in point two batteries connected in series.

However, to make calculations easier it is useful to establish a ground reference and take all measurements relative to this common node.

This discussion of "ground" is interesting. You may want to look at https://en.wikipedia.org/wiki/Ground_(electricity)

Regards,

APD
(5 votes)
• So we were told that current flows from negative to positive... If that's the case, how can it flow from 0V to 10V? Isn't it the case that the minus terminal is at a higher potential energy point than the positive one? Otherwise how could the current flow from minus to plus? And why don't you guys talk about the way things behave in the real world? If it is minus to plus say so...
(3 votes)
• When you are dealing with a potential field you need to understand how a charge interacts with that field. The electric potential increases as you go negative to positive for a positive charge but it decreases for a negative charge.
(2 votes)

## 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.