Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

Mesh Analysis of AC Circuit

The nodal analysis of ac circuit, we will not cover the basic explanation of its principle. You have to read the link above in order to understand ‘how to use it’ properly.
Let us review the examples below to be able to analyze the ac circuit using mesh analysis.
Determine current I_o in the circuit of Figure. using mesh analysis.
Example of mesh analysis for ac circuit 

Applying KVL to mesh 1, we obtain
..... (1.1) 
For mesh 2,
.....(1.2) 
For mesh 3, I₃ = 5. Substituting this to Equations.(1.1) and (1.2), we obtain
..... (1.3) 
.....(1.4) 
Equations.(1.3) and (1.4) can be rewritten in matrix form as

and its determinants are

The desired current is

Supermesh Analysis of AC Circuit

Next, we will analyze an ac circuit with supermesh within it.
Before doing that, make sure you have understood the principle of supermesh analysis first.
Solve for V_o in the circuit of Figure. with mesh analysis.
Example of supermesh analysis for ac circuit 

As shown above, meshes 3 and 4 form a supermesh due to the current source between the meshes. For mesh 1, KVL results

or
......(2.1)
For mesh 2,
... (2.2) 
For the supermesh,
... (2.3) 
Due to the current source between meshes 3 and 4, at node A,
.... (2.4) 
We reduce the above four equations to two by elimination, instead of solving them directly.
Combining Equations.(2.1) and (2.2),
.....(2.5) 
Combining Equations.(2.2) to (2.4),
....(2.6) 
Analysis circuit in Figure 

From Equations.(2.5) and (2.6), we obtain the matrix equation

We obtain the determinants

Current I₁ is obtained as

The required voltage V_o is