Mesh Analysis with Current Sources

Mesh analysis is simpler in circuits with current sources because they require fewer equations for analysis.

Consider a two-mesh circuit with a current source in only one mesh.

The mesh currents are assigned, and the branch containing the current source is excluded from mesh analysis.

Kirchhoff's voltage law is applied to the remaining mesh to obtain a linear equation.

As the current in the second mesh is equal in magnitude but opposite in direction to the source current, the simplified equation allows for determining the current in the first mesh.

Now, consider another circuit with a current source between both meshes.

A larger supermesh is created by excluding the current source and elements connected in series with it.

Again, applying Kirchhoff's voltage law to the supermesh results in a linear equation.

Additionally, Kirchhoff's current law is applied to a node where the branch with the current source is connected, yielding another linear equation that links the two branch currents.

The solutions of the simultaneous equations provide the values of the mesh currents.