What is a supermesh?

In a regular mesh analysis, you analyze each closed loop separately by applying Kirchhoff's voltage law (KVL) around the loop to obtain equations relating the voltages across different elements. However, in some circuits, there might be current sources that share two meshes, which complicates the traditional mesh analysis approach.

To overcome this issue, a supermesh is formed by combining two adjacent meshes that share a current source. The combination is done in such a way that the voltage drop across the current source becomes the sum of the voltages across the elements in both meshes.

The key steps to analyze a circuit using supermesh are as follows:

Identify the meshes in the circuit and label them as usual.

If there are current sources that are shared by two adjacent meshes, identify them.

Create a supermesh by combining the two meshes that share the current source. To do this, consider the current source as a "super" element with zero resistance and zero voltage drop.

Apply KVL around the supermesh, accounting for the voltage sources and resistances within the supermesh.

Solve the resulting equations to determine the unknown currents and voltages in the circuit.

Using supermesh simplifies the analysis of certain circuits, particularly when dealing with circuits that have current sources shared between meshes. It allows engineers and students to effectively analyze and solve circuits without getting tangled up in complex algebraic manipulations.