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 Io in the circuit of Figure. using mesh analysis.
Example of mesh analysis for ac circuit Example of mesh analysis for ac circuit 

Applying KVL to mesh 1, we obtain
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)..... (1.1) 
For mesh 2,
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE).....(1.2) 
For mesh 3, I= 5. Substituting this to Equations.(1.1) and (1.2), we obtain
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)..... (1.3) 
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE).....(1.4) 
Equations.(1.3) and (1.4) can be rewritten in matrix form as
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)
and its determinants are
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)
The desired current is
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

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 Vo in the circuit of Figure. with mesh analysis.
Example of supermesh analysis for ac circuit 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 & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)
or
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)......(2.1)
For mesh 2,
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)... (2.2) 
For the supermesh,
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)... (2.3) 
Due to the current source between meshes 3 and 4, at node A,
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE).... (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 & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE).....(2.5) 
Combining Equations.(2.2) to (2.4),
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)....(2.6) 
Analysis circuit in Figure Analysis circuit in Figure 

From Equations.(2.5) and (2.6), we obtain the matrix equation
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)
We obtain the determinants
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Current I1 is obtained as
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)
The required voltage Vo is
Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

The document Mesh & Supermesh for AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
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FAQs on Mesh & Supermesh for AC Circuits - Network Theory (Electric Circuits) - Electrical Engineering (EE)

1. What is mesh analysis in AC circuits?
Ans. Mesh analysis is a method used to analyze AC circuits by dividing the circuit into loops called meshes. Each mesh is assigned a current variable, and Kirchhoff's voltage law is applied to write equations for each mesh. These equations can then be solved simultaneously to determine the unknown currents in the circuit.
2. How is mesh analysis different from nodal analysis in AC circuits?
Ans. In mesh analysis, the circuit is divided into loops, whereas in nodal analysis, the circuit is divided into nodes. Mesh analysis involves writing equations based on Kirchhoff's voltage law, while nodal analysis involves writing equations based on Kirchhoff's current law. The choice between mesh analysis and nodal analysis depends on the complexity and structure of the circuit.
3. What is a supermesh in AC circuits?
Ans. A supermesh is a combination of two or more meshes in a circuit that share a current source. When analyzing a circuit with a supermesh, the current source is treated as an unknown variable, and a modified equation is written for the combined mesh. This allows for a more simplified analysis of the circuit.
4. How do you handle dependent sources in mesh analysis of AC circuits?
Ans. Dependent sources in mesh analysis are treated similarly to independent sources. The dependent source is included in the equation for the corresponding mesh, just like any other source. The only difference is that the value of the dependent source may be expressed in terms of other circuit variables, which can be substituted into the equation during the solution process.
5. What are the limitations of mesh analysis in AC circuits?
Ans. Mesh analysis has a few limitations in AC circuits. It assumes that all circuit elements are linear, which means it may not be applicable to circuits with non-linear components. Additionally, mesh analysis requires the circuit to be planar, meaning all the elements lie on a single plane. If the circuit is not planar, alternative methods such as nodal analysis may need to be used.
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