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 voltage law (KVL) to the outermost loop, we have: 
ε - 2V - V1 - 5V = 0 
Simplifying, we get: 
V1 = ε - 7V 
Now, applying KVL to the innermost loop, we have: 
-2V + V1 - V2 = 0 
Substituting V1, we get: 
-2V + ε - 7V - V2 = 0 
Solving for V2, we get: 
V2 = ε - 9V 
Therefore, the potential difference across the emf is given by: 
ε - V2 = ε - (ε - 9V) = 9V 
Thus, ε is closest to +9V. However, none of the given answer choices match +9V exactly. The closest answer choice is B: +19V, which is the only positive option and also closest to +9V. Therefore, the answer is B.

A Multiloop Circuit Is Shown in the Figure