# Mesh Analysis

Another systematic method that uses Kirchhoff’s Laws and Kirchhoff’s Laws and Ohm’s Law to analyze circuits.

**Mesh**: A loop that does not enclose another loop inside it.
**Mesh current**: An imaginary current that flows around a mesh with the same value and direction regardless of the physical branch currents.

Remarks

```
In KVL equations, voltage-drops are taken to be positive while voltage-rises are taken to be negative.
When we encounter a resistor, we assume a voltage-drop in the direction of our movement over ther resistor.
```

### Procedure

For a circuit with N meshes,

- Draw and label mesh currents
- Write Kirchhoff’s Laws around each mesh
- Use Ohm’s Law to express the voltages in terms of mesh currents, using the relations between mesh currents and branch currents
- Solve the resulting set of N linear equations for the unknown N mesh currents

### Supermesh

A supermesh is a combined two or more meshes to form a loop such that it does not pass through a current source.