Mesh Analysis - Procedure, Problems

What is Mesh Analysis?

Loop is nothing but any closed path. A loop is said to be a mesh if it is not having any other loop inside it. In the Mesh analysis method, we will analyze the currents of meshes present in the given electric circuit. Hence, we can call this method a mesh current analysis method or Mesh analysis in short. 

Similarly, in the Loop analysis method, we will analyze the currents of loops present in the given electric circuit. Hence, we can call this method the Loop current analysis method or Loop analysis in short. Since the number of mesh equations will always be less than or equal to the number of loop equations, we will prefer Mesh analysis compared to Loop analysis.

The procedure of Mesh Analysis

We can solve some of the network theory problems easily by using the Mesh Analysis method. Here, first, you will get to know that the Mesh analysis is based on which laws & then the method Mesh analysis is generally used to determine which electrical quantities etc. Now, let’s see the steps for solving the given network in the Mesh Analysis method.

• Step 1: Observe the number of meshes present in the given circuit and then represent the current in each mesh either in a clockwise direction or in the anti-clockwise direction.
• Step 2: Represent the current flows through each element of the given circuit in terms of the mesh currents.
• Step 3: Write the mesh equation (KVL & Ohm’s law) for every mesh, whose mesh current is unknown.
• Step 4: Get the mesh currents by solving the above mesh equations. By using these mesh currents, we can find the response (voltage or current) of any branch present in the given circuit.

Mesh Analysis Problems

Question 1: Find the current, I of the following electric circuit by using the Mesh analysis method.

Solution: Step 1: In the given electric circuit, there are 3 meshes. For the time being, let us consider the mesh currents in a clockwise direction.

Step 2: In the following diagram, the current flowing through each element of the given circuit is represented in terms of the mesh currents.

Step 3: We no need to write the mesh equations for meshes 1 and 3. Rather, we can directly write the mesh current values by looking at the branch currents. 

i₁ = 2 A and i₃ = 5 A

Mesh equation around Mesh 2 is

-i₂(1)-(i₂-i₃)(1)-(i₂-i₁)(1)=0

=>-i₂(1)-(i₂-5)(1)-(i₂-2)(1)=0

=>3i₂=7

=>i₂=7/3 A

Step 4: The current, I = i₂-2 = 7/3-2 = 1/3 A. So, by using the Mesh analysis method, we got the value of current I as 1/3 A. 

Question 2. Find the current, I of the following electric circuit by using the Mesh analysis method.

Solution: Step 1: In the given electric circuit, there are 2 meshes. For the time being, let us consider the mesh currents in a clockwise direction.

Step 2: In the following diagram, the current flowing through each element of the given circuit is represented in terms of the mesh currents.

Step 3: Mesh equation around Mesh 1 is 

20-i₁(10)-(i₁-i₂)10- 5 = 0

=>20i₁-10i₂=15

=>4i₁-2i₂=3   …(1)

Mesh equation around Mesh 2 is

-20 i₂+5-(i₂-i₁)10=0

=>10 i₁-30i₂ = -5

=>2 i₁-6i₂ = -1  …(2)

Step 4: By solving equations (1) and (2), we will get i₁=1 A & i₂=0.5 A.

=>I=i₂=0.5 A. So, by using Mesh analysis method, we got the value of current I as 0.5 A. 

In this article, we discussed the Mesh analysis method for DC circuits, and then we solved the Mesh analysis problems for DC circuits. Similarly, we can apply the Mesh analysis method for AC circuits and also solve the Mesh analysis problems in AC circuits. 

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