Question 2.15: Solve for the currents in the circuit of Figure 2.41(a), whi...

First, we write equations for the mesh currents as we have done for independent sources. Since there is a current source common to mesh 1 and mesh 2, we start by combining the meshes to form a supermesh and write a voltage equation:

−20 + 4i_1 + 6i_2 + 2i_2 = 0          (2.67)

Then, we write an expression for the source current in terms of the mesh currents:

av_x = 0.25v_x = i_2 − i_1    (2.68)

Next, we see that the controlling voltage is
v_x = 2i_2    (2.69)

Using Equation 2.58 to substitute for v_x in Equation 2.57, we have

20(i_3 − i_1) + 14i_3 + 12(i_3 − i_2) = 0            (2.58)

10(i_2 − i_1) + 12(i_2 − i_3) + 42 = 0            (2.57)

\frac{i_2}{2} = i_2 -i_1            (2.70)

Finally, we put Equations 2.67 and 2.70 into standard form, resulting in

4i_1 + 8i_2 = 20
i_1-\frac{i_2}{2}=0
Solving these equations yields i_1 = 1 A and i_2 = 2 A.