Q. In the circuit shown in the figure reading of voltmeter is $V_{1}$ when only $S_{1}$ is closed, reading of voltmeter is $V_{2}$ when only $S_{2}$ is closed and reading of voltmeter is $V_{3}$ when both $S_{1}$ and $S_{2}$ are closed. Then
A) $V_{3} > V_{2} > V_{1}$
B) $V_{2} > V_{1} > V_{3}$
C) $V_{3} > V_{1} > V_{2}$
D) $V_{1} > V_{2} > V_{3}$
Explanation
(b) In series : Potential difference $\propto R$
When only $S_{1}$ is closed $V_{1} = \frac{3}{4}E = 0.75E$
When only $S_{2}$ is closed $V_{2} = \frac{6}{7}E = 0.86E$
And when both $S_{1}$ and $S_{2}$ are closed combined resistance of $6R$ and $3R$ is $2R$
$\therefore V_{3} = \left( \frac{2}{3} \right)E = 0.67E \Rightarrow V_{2} > V_{1} > V_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.