Question 3.7: For the circuit in Fig. 3.24, find i1 to i4 using mesh ana......

Note that meshes 1 and 2 form a supermesh since they have an independent current source in common. Also, meshes 2 and 3 form another supermesh because they have a dependent current source in common. The two supermeshes intersect and form a larger supermesh as shown. Applying KVL to the larger supermesh,

2i_{1} + 4i_{3} + 8(i_{3} – i_{4} ) + 6i_{2} = 0

or

i_{1} + 3i_{2} + 6i_{3} – 4i_{4} = 0            (3.7.1)

For the independent current source, we apply KCL to node P:

i_{2} = i_{1} + 5               (3.7.2)

For the dependent current source, we apply KCL to node Q:

i_{2} = i_{3} + 3 I_{o}

But I_{o} = -i_{4} , hance ,

i_{2} = i_{3} – 3i_{4}               (3.7.3)

Applying KVL in mesh 4,

2i_{4} + 8(i_{4} – i_{3} ) + 10 = 0

or

5i_{4} – 4i_{3} = -5                       (3.7.4)

From Eqs. (3.7.1) to (3.7.4),