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 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

**I**_{o}in the circuit of Figure.(1) using mesh analysis.Figure 1. Example of mesh analysis for ac circuit |

Applying KVL to mesh 1, we obtain

(1.1) |

For mesh 2,

(1.2) |

For mesh 3,

**I**_{3}= 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 understand the principle of supermesh analysis first.

Solve for

**V**_{o}in the circuit of Figure.(2) with mesh analysis.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

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) |

Figure 3. Analysis circuit in Figure.(2) |

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

We obtain the determinants

Current

**I**_{1}is obtained as
The required voltage

**V**_{o}is
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