If E1 = 13.0 V and E2 = 5.0 V, calculate the current I2 flowing in emf source E2.

The solution would be like this for this specific problem:

KCL at Junction a.

+ I1 + I2 + I3 = 0 (1)

KVL

+ 13 V - 0.2 R I1 - 0.025 R I1 - 5 V + 0.02 R I2 = 0 (2)

8 + 0.02 I2 = 0.225 I1

I1 = 35.6 + 0.0889 I2 (2A)

KVL (bottom loop - CCW direction)

- 0.02 R I2 + 5 V + 0.5 R I3 = 0 (3)

0.5 I3 = - 5 + 0.02 I2

I3 = - 10 + 0.04 I2 (3A)

Replace 2A and 3A into 1.

+ I1 + I2 + I3 = 0

(35.6 + 0.0889 I2) + I2 + (-10 + 0.04 I2) = 0

1.129 I2 = - 25.6

I2 = - 22.6A

Solve 2A and 3A for other currents.

I1 = 35.6 + 0.0889 I2 = 35.6 + 0.0889 * - 22.6 = 33.5A

I3 = - 10 + 0.04 I2 = - 10 + 0.04 * - 22.6 = - 10.9A

So the answer is letter D.