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## AP®︎/College Physics 1

### 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

TermMeaning
LoopClosed 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:
$\mathrm{\Sigma }\mathrm{\Delta }V=0$

### 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 $ϵ$. 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 $ϵ$:
$\begin{array}{rl}\mathrm{\Sigma }\mathrm{\Delta }V& =0\\ \\ -{V}_{1}-{V}_{2}+ϵ& =0\\ \\ {V}_{2}& =ϵ-{V}_{1}\end{array}$