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,

1. Draw and label mesh currents
2. Write Kirchhoff’s Laws around each mesh
3. Use Ohm’s Law to express the voltages in terms of mesh currents, using the relations between mesh currents and branch currents
4. 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.