MESH ANALYSIS

Mesh Analysis

Mesh analysis is a method that is used to solve planar circuits for the currents  at any place in the circuit. Planar circuits are circuits that can be drawn on a plane surface with no wires crossing each other. Mesh analysis use Kirchhoff’s voltage law to arrive at a set of equations guaranteed to be solvable if the circuit has a solution.

Using mesh currents instead of element currents as circuit variables is convenient and reduces the number of
equations that must be solved simultaneously. Recall that a loop is a closed path with no node passed more than once. A mesh is a loop that does not contain any other loop within it.

A mesh is a loop which does not contain any other loops within it.

Steps to Determine Mesh Currents:

1. Assign mesh currents to the n meshes.

2. Apply KVL to each of the n meshes. Use Ohm’s law to express the voltages in terms of the mesh currents.

3. Solve the resulting n simultaneous equations to get the mesh currents.

Mesh Analysis with Current Sources

Two possible cases:

• CASE 1 : When a current source exists only in one mesh.

• CASE 2 : When a current source exists between two meshes:  We create a SUPERMESH by excluding the current source and any elements connected in series with it.

A supermesh results when two meshes have a (dependent or independent) current source in common.