A multiloop circuit is shown in the figure. Some circuit quantities are not labeled. It is not necessary to solve the entire circuit. The emf ε is closest to
A) +3 V.
B) +19 V.
C) -3 V.
D) -10 V.
E) -1 V.

Question

A multiloop circuit is shown in the figure. Some circuit quantities are not labeled. It is not necessary to solve the entire circuit. The emf ε is closest to 
A) +3 V. 
B) +19 V. 
C) -3 V. 
D) -10 V. 
E) -1 V.

Quizplus · Accepted Answer

Using Kirchhoff's loop rule, we can write:
-ε + 6I1 - 4I2 = 0 (loop 1)
4I2 - 2I3 - 4I4 = 0 (loop 2)
2I3 - 3I1 = 0 (loop 3)
where I1, I2, I3, I4 are the currents flowing in loops 1, 2, 3 and the small loop in the bottom right corner, respectively.
From loop 3, we get I3 = (3/2)I1.
Substituting this into loop 2, we get I2 = (2/3)I1.
Substituting the above values into loop 1, we get ε = 8I1/3.
Therefore, ε is positive and closest to 19 V (choice B) when I1 is positive.

A Multiloop Circuit Is Shown in the Figure