## Kirchhoff’s Rules

6.3 Kirchhoff’s Rules

### Learning Objectives

By the end of this section, you will be able to:

- State Kirchhoff’s junction rule
- State Kirchhoff’s loop rule
- Analyze complex circuits using Kirchhoff’s rules

### Kirchhoff’s Rules

There are two circuit analysis rules that can be used to analyze any circuit, simple or complex. These rules are special cases of the laws of conservation of charge and conservation of energy. The rules are known as Kirchhoff’s rules, after their inventor Gustav Kirchhoff (1824–1887).

- Kirchhoff’s first rule is a statement of conservation of current (charge): “whatever current goes in, must come out”.
- Kirchhoff’s second rule says “The sum of voltage changes around any closed loop is always zero”. (This is just conservation of energy.)

Here is a drawing to show what we mean by the current that goes into a junction equals the current that comes out:

And here is a reminder of the loop rule:

We’ve actually been using these rules in our analysis of circuits so far. But they come in handy when you have a circuit that cannot be simplified down to one equivalent resistor. Here is an example:

Here are some rules to follow so that you always get the correct answer when analyzing one of these problems:

In the following video I work out the solution to this circuit, following these rules.

**Practice!**

Practice 6.3.1 |
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What is the current through the 30 Ω resistor? |

Practice 6.3.2 |
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What is the current through the 20 Ω resistor? |

Practice 6.3.3 |
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What is the current through the 10 V battery? |