Question

In the circuit below, the potential difference between $A$ and $B$ is

• A. $10V$
• B. $20V$
• C. $30V$
• D. $40V$

Answer 1

Answer: (A)

Let the charges flowing be $q_1$ and $q_2$ in loops $I$ and $II$ respectively.
Applying Kirchhoff loop law in loop $I$ :
$\frac{q_1}{1}+\frac{q_1+q_2}{3}-190=0$
$⟹4q_1+q_2=190\times 3$
Applying Kirchhoff loop law in loop $II$ :
$\frac{q_1+q_2}{3}+\frac{q_2}{3}+\frac{q_2}{1}=0$
$⟹q_1=-5q_2$
Putting this in equation 1, we get $4(-5q_2)+q_2=190\times 3$
$⟹q_2=30\mu C$
Thus potential difference $V_{AB}=\frac{q_2}{3\mu F}=\frac{30\mu C}{3\mu F}=10V$