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 + 6V + 4V - 2V + 2I + 8V = 0
Simplifying, we get:
I = (ε - 16V) / 2
Using Kirchhoff's junction rule at the top junction, we can write:
I + 2V - 4V = 0
Simplifying, we get:
I = 2V
Substituting this value of I in the earlier expression, we get:
2V = (ε - 16V) / 2
Solving for ε, we get:
ε = 19V
Therefore, the closest option is B (+19V).

A Multiloop Circuit Is Shown in the Figure