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

Lesson 4: Kirchhoff's loop rule# Kirchhoff's loop rule review

Review the key terms and skills related to Kirchhoff's loop rule, including how to determine the electric potential difference across a component.

## Key terms

Term | Meaning | |
---|---|---|

Loop | Closed circuit that starts and ends at the same point. |

## Kirchhoff’s loop rule

Kirchhoff’s loop rule states that the sum of all the electric potential differences around a loop is zero. It is also sometimes called Kirchhoff’s voltage law or Kirchhoff’s second law. This means that the energy supplied by the battery is used up by all the other components in a loop, since energy can’t enter or leave a closed circuit. The rule is an application of the conservation of energy in terms of electric potential difference, $\mathrm{\Delta}V$ .

Mathematically, this can be written as:

### How to determine the electric potential difference across a circuit component

For example, we can use Kirchhoff’s loop rule to find the unknown electric potential difference across a resistor (Figure 1).

Let’s pick our starting point at the battery and go around the loop until we are back to the same point.

The electric potential increase over the battery is $\u03f5$ .
Over ${R}_{1}$ there is an electric potential decrease of ${V}_{1}$ .
We do not know the electric potential decrease ${V}_{2}$ over ${R}_{2}$ .

Now we can use the loop rule to solve for ${V}_{2}$ in terms of ${V}_{1}$ and $\u03f5$ :

## Learn more

For deeper explanations, see our video on Kirchhoff's loop rule (or voltage law).

To check your understanding and work toward mastering these concepts, check out our exercises:

## Want to join the conversation?

- I am trying to master Kirchoff's loop rule, but I don't understand how you setup the loop.

A loop is a closed circuit where you start and end at the same point. But I don't understand... sometimes they use an left loop, sometimes a right loop, sometimes and outer loop, ect.

Can I please get clarification on how to use Kirchoff's voltage/loop law?

Thanks! :)(5 votes)- You can use any loop you want. You just have to make sure that your signs are right and you do the correct operations. Once you take a loop, you need to identify your voltage sources and your resistors. The sum of the voltage drops across the resistors must equal to the total voltage that the current starts out with. Hope this helps!(7 votes)

- how do i master Kirchhoff's rule?

ways to simplify the whole concept.(2 votes)- Practise is the only key. Start from khan academy's practise sheets, they are the of the lowest level, designed to introduce concept and then increase your level slowly from various problems from different books or other sources.(13 votes)

- In some of the practice questions with multiple loops there was a voltage rise around loops without an additional voltage source. How is it possible that the current would flow against the given flow from the one voltage source??(3 votes)
- is there any way to learn this law easily(2 votes)
- Okay, isn't it the electrostatic force that pushes the electrons to flow through the circuit? in that, the electrons repel each other and try to go towards the other end of the battery(positive side)? So doesn't that make the positive side of the battery the final destination of the electrons? So why do they loop around even after finally arrived at the battery?(1 vote)
- In a circuit, it is really electrons that are flowing. However, back in the day when they experimented with circuits, they didn't know what electrons were. So, they defined currents as the flow of positive charge. So, for now, lets just imagine that positive charges are flowing through the circuit. The positive terminal of the battery "pushes" the positive charge through the circuit and to the negative terminal. Then the battery does work on the charge to get it from the negative terminal to the positive terminal. When the charge reaches the positive terminal, it has gained the full voltage of the battery and is ready to go through the circuit again. Hope this helps!(3 votes)

- ohm's law states that potential difference across a conductor is directly proportional to the current (provided temperature is constant)(1 vote)

- How we can anderstand in simple way(0 votes)