Solve for the mesh currents defined in the circuit in Fig So

Solve for the mesh currents defined in the circuit in Fig.

Solution

There are four meshes!!!

applying mesh analysiss to the above circuit we get;

mesh on firs loop!!!

2I₁+4(I₁-I₂)+7(I₁-I₃)+V_X=O

applying mesh on the second loop

3I₂+4I₂+8(I₂-I₄)+4(I₂-I₁)=3I_X

applying mesh to the third loop!!!

7(I₃-I₁)+2(I₃-I₄)+2V_X=0

applying mesh analysis to 4th mesh

8(I₄-I₁)+2(I₄-I₃)=12=0

on solving the above four equations we can get the respective currents