Maxwell Mesh method Solved problem with Examples

Definition

This method involves a set of independent loop current assigned to as many Maxwell mesh meshes as it exist in the circuit and these currents are employed in connection with appropriate resistances when the KVL equation are written.

Circuit theory Example :

 Using KVL :

• For the loop A : E1 - IA.(R1+R3) - I3.R3 = 0
• For the loop B : E2 - IB.(R2+R3) - IA.R3 = 0

Note: mesh currents IA and IB are evaluated by simultaneous substitutions of the equations formulated from each loop or mesh using KVL.

I1 = |IA|     I2 = |IB|     I2 = |IA + IB|

Solved problem :

Solve this circuit for V using Maxwell's mesh method.

• 4.0 V
• 5.2 V
• 2.6 V
• 3.5 V

Solution and circuit analysis:

Re-draw the circuit:

Apply KVL on the loop 'dabcd'

(IA - IB)2 - IB(8) - (IB + IC)2 = 0
Note : IA = 6A ; IC = 3A

Substitute:
(6 - IB).2 - 8.IB - (IB + 3).2 =0
12 - 2.IB - 8IB - IB - 6 = 0
IB = 0.5 A

V = IB(8) = 0.5 x 8
V = 4 Volts