Problem 4-34

Use mesh analysis to find the power delivered by the dependent source.

Mesh currents were chosen as shown in green on the diagram.

Define the current i_f in terms of the mesh currents.

i_f = I_B - I_C

No current sources, thus no supermeshes.

Write KVL around the three meshes.

Mesh A:

1 I_A + 3 (I_A - I_C) + 2 (I_A - I_B) - 132 = 0
6 I_A - 2 I_B - 3 I_C= 132 (equation 1)

Mesh B:

2 (I_B - I_A) + 10 (I_B - I_C) - 7 (i_f) = 0
2 (I_B - I_A) + 10 (I_B - I_C) - 7 (I_B - I_C) = 0
- 2 I_A + 5 I_B - 3 I_C = 0 (equation 2)

Mesh C:

5 I_C + 10 (I_C - I_B) + 3 (I_C - I_A) = 0
- 3 I_A - 10 I_B+ 18 I_C = 0 (equation 3)

Solving the three equations gives (details not shown here)

I_A = 48 A
I_B = 36 A
I_C = 28 A

Now find the power developed by the dependent source. Remember, power developed is P_dev = VI if the arrow LEAVES the positive reference.

P_dev = (7 i_f) (I_B)
P_dev = 7 (I_B - I_C) (I_B)
P_dev = 7 (36 - 28) (36)
P_dev = 2016 W