# Mesh Analysis

By Mona Kumari|Updated : September 30th, 2022

Mesh Analysis is one of the important methods for solving Network theory problems. The method we use for solving the given electrical network / electric circuit or the method we use for analyzing the given electrical network / electric circuit is known as the Method of Analysis.

In this article, get an overview of the Mesh analysis method and how to solve an electric circuit/network problem by using this method. Here, first, you will get to know what Mesh analysis is and then the procedure of this method. In this article, we discussed the problems with Mesh analysis as well.

## 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. The mesh analysis is based on Kirchhoff's Voltage Law.

### Mesh Analysis Definition

In the Mesh analysis method, we will analyze the currents of meshes in the given electric circuit. Hence, mesh analysis is equal to a mesh current analysis method. 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 prefer Mesh analysis to Loop analysis.

## Procedure of Mesh Analysis

We can easily solve network theory problems 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 in the given circuit and then represent the current in each mesh either in a clockwise or in anti-clockwise direction.
• Step 2: Represent the current flows through each circuit element 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. Using these mesh currents, we can find the response (voltage or current) of any branch in the given circuit.

## Mesh Analysis Solved Problems

Question 1: For the following circuit, find the current through the ammeter by using Mesh Analysis. 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 circuit element 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, using the Mesh analysis method, we got the current I value 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 circuit element 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, using the Mesh analysis method, we got the current I value as 0.5 A.

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

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## FAQs on Mesh Analysis

• The mesh analysis is nothing but the combination of KVL and ohm’s law. For any mesh, we can write the KVL equation first and then use ohm’s law in that equation wherever required. This resulting equation is known as the mesh equation. So, we can directly write the mesh equation for any mesh by using KVL and ohm’s law together.

• In the Mesh analysis method, we will write the mesh equations to find the unknown mesh currents. So, the minimum number of mesh equations required will be the same as that of the number of unknown mesh currents.

• For the given electric circuit, if the number of mesh equations to be solved is less than that of the number of nodal equations to be solved, then we can prefer the Mesh analysis method compared to the Nodal analysis method.

• By using Mesh analysis, we can determine the mesh currents first. And then by using these mesh currents, we can calculate the response (voltage or current) of any element present in the given circuit.

• A circuit is said to be a planar circuit, if we can draw that circuit in two-dimensional plane without having any crossovers. Otherwise, it is said to be a non-planar circuit. So, Mesh analysis can be applied only for planar circuits.

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