Mesh Analysis

The mesh analysis technique consists of the steps stated below

1. Transform all the currents sources to voltage sources, if possible

2. Identify and assign the current to each mesh of network (preferably in same direction).

3. Write down the mesh equations by using KVL and simplify them.

4. Solve the system of equations.

5. Number of equations is equal to the number of meshes in network.

Solution: Mesh Analysis

3 meshes can be identified with currents I₁,I₂ and I₃ as shown in Figure where all the currents are assumed to be flowing in the clockwise direction.
 

For mesh analysis, 3 loops are highlighted having currents I₁,I₂ and I₃. Observe the common (shared) circuit elements between the meshes such as R2 (between meshes 1 and 2) and R3 (among meshes 2 and 3). The current through R2, for instance, will be I1 - I2 when considering mesh 1 whilst it will be I₂ - I₁ for mesh 2.

The KVL equations can be written as follows

Substitute given values of resistors and voltage source,
 
The solution of above equations can be obtained by substitution or by Cramer's rule or matrix method.
 

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