If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## 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?
• 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
• Why is it that if the resistances are equal (100 ohm and 100 ohm) , the voltage gets halved to 5V?
• 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.
• What is the reason for this voltage drop?
• 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!
• Why is the bottom node at 0 volts?
• 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.
• 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.
• Sal says the current is the same everywhere in a 1-loop circuit, not voltage.
• What does 0 Volts mean? Is it possible to have a circuit running with 0 Volts in one path as shown?
• 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.
• 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?
• 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.
• 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.
• 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.
• Is the voltage always 0 for the node that goes into the minus side of the voltage source?
• 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
• 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...
• 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.