Page 128 - Basic Electrical Engineering

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 be flowing 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 us calculate the current
flowing through the branches in the circuit given in Fig. 2.26.

Figure 2.26

We have assumed loop currents I and I flowing in the clockwise direction
1
2
as shown.
It may be noted that current flowing through the resistor R is the algebraic
3
sum of the two currents I and I . Here I is flowing in the downward
1
1
2
direction while I is flowing in the upward direction.
2
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

12 − 4 I − 8(I − I ) = 0
1
2
1
or, 3 I − 2 I = 3 (i)
1
2