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

Applying Kirchhoff's loop rule to the larger loop, we get:
ε - 4IR - 3I = 0
Applying Kirchhoff's loop rule to the smaller loop, we get:
-3I + 6IR = 0
Solving these two equations simultaneously, we get:
I = 3/2 A
Substituting this value of I in the equation for the larger loop, we get:
ε = 19 V.

A Multiloop Circuit Is Shown in the Figure