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What is the Mesh Analysis AC Circuit Formula?

Kirchhoff's voltage law (KVL) forms the basis of mesh analysis. The validity of KVL for ac circuit can be seen in Mesh Analysis for dc circuit here. Keep in mind that the very nature of using mesh analysis is that it is to be applied to planar circuit.
mesh analysis ac circuit

Mesh Analysis of AC Circuit

Like 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 ac circuit using mesh analysis.

Determine current Io in the circuit of Figure.(1) using mesh analysis.
mesh analysis ac circuit
Figure 1. Example of mesh analysis for ac circuit
Applying KVL to mesh 1, we obtain
mesh analysis ac circuit
(1.1)
For mesh 2,
mesh analysis ac circuit
(1.2)
For mesh 3, I3 = 5. Substituting this to Equations.(1.1) and (1.2), we obtain
mesh analysis ac circuit
(1.3)
mesh analysis ac circuit
(1.4)
Equations.(1.3) and (1.4) can be rewritten in matrix form as
mesh analysis ac circuit
and its determinants are
mesh analysis ac circuit
The desired current is
mesh analysis ac circuit

Supermesh Analysis of AC Circuit

Next we will analyze an ac circuit with supermesh within it. Before doing that, make sure you have understand the principle of supermesh analysis first.

Solve for Vo in the circuit of Figure.(2) with mesh analysis.
mesh analysis ac circuit
Figure 2. 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
mesh analysis ac circuit
or
mesh analysis ac circuit
(2.1)
For mesh 2,
mesh analysis ac circuit
(2.2)
For the supermesh,
mesh analysis ac circuit
(2.3)
Due to the current source between meshes 3 and 4, at node A,
mesh analysis ac circuit
(2.4)
We reduce the above four equations to two by elimination, instead of solving them directly.
Combining Equations.(2.1) and (2.2),
mesh analysis ac circuit
(2.5)
Combining Equations.(2.2) to (2.4),
mesh analysis ac circuit
(2.6)
mesh analysis ac circuit
Figure 3. Analysis circuit in Figure.(2)
From Equations.(2.5) and (2.6), we obtain the matrix equation
mesh analysis ac circuit
We obtain the determinants
mesh analysis ac circuit
Current I1 is obtained as
mesh analysis ac circuit
The required voltage Vo is
mesh analysis ac circuit

Untuk Bahasa Indonesia baca Analisis Mesh Rangkaian AC
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