# Mesh Current Analysis with Dependent Voltage Source

**1. The problem statement, all variables and given/known data**

Use the mesh-current method to find the power developed in the dependent voltage source in the circuit in figure (Figure 1) if v = 29V.

**2. Relevant equations**

∑R in mesh 1 * i_1 – ∑R in common between meshes 1 and 2 * i_2 = v_source in mesh 1

∑R in mesh 2 * i_2 – ∑R in common between meshes 1 and 2 * i_1 = v_source in mesh 2

P = i*v

**3. The attempt at a solution**

Putting mesh 1 on the top, mesh 2 on the left, and mesh 3 on the right, I have:

Mesh 1:

(3+5)*i_1 – 3*i_2 -5*i_3 = 53*i_delta

Mesh 2:

(3+20+7)*i_2 – 3*i_1 – 20*i_3 = 29

Mesh 3:

(5+20+2)*i_3 – 5*i_1 – 20*i_2 = -29

Aux:

i_2 = i_delta + i_3

Solving, I got i_1 = 7.84, i_2 = 3.96, i_3 = 3.3, and i_delta = 0.658

V_dependent = 53*i_delta = 34.3

P = i*V = 7.84 * 34.3 = 269 W (incorrect)

Any ideas?

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