Maxwell’s Mesh Current Method

Maxwell’s Mesh Current Method

Posted by Prabhat Jani on 09:15 in Basic, Basic Electrical Engg, Circuit Analysis

A mesh is a smallest loop in a network. KVL is applied to each mesh in terms of mesh currents instead of branch currents. As a convention, mesh currents are assumed to beflowing in the clockwise direction without branching out at the junctions. Applying KVL, the voltage equations are framed. By knowing the mesh currents, the branch currents can be determined. The procedure followed is explained through an example. Let uscalculate the current flowing through the branches in the circuit given in Fig. 2.26.

Figure 2.26

We have assumed loop currents I₁ and I₂ flowing in the clockwise direction as shown.

It may be noted that current flowing through the resistor R₃ is the algebraic sum of the two currents I₁ and I₂. Here I₁ is flowing in the downward direction while I₂ is flowing in the upward direction.

We will now write the voltage equations for the two loops applying KVL and then solve the equations. If the value of any mesh currents is calculated as negative, we will take the direction of that mesh current opposite to the assumed clockwise direction.

For loop DABCD, the voltage equation is

For loop BEFCB, the voltage equation is

solving eqs. (i) and (ii), we get

and current flowing through R₃ is (I₁ − I₂) = 0.91 A

I₁ is flowing through R₁, I₂ is flowing through R₂ and (I₁ − I₂) is flowing through R₃.