Question

In the circuit shown in the figure, reading of voltmeter is $V_1$ when only $S_1$ is closed, $V_2$ when only $S_2$ is closed and $V_3$ when both $S_1$ and $S_2$ are closed. Choose the correct relation between $V_1$, $V_2$ and $V_3$.

• A. $V_2>V_1>V_3$
• B. $V_3>V_2>V_1$
• C. $V_3>V_1>V_2$
• D. $V_1>V_2>V_3$

Answer 1

The correct option is A

$V_2>V_1>V_3$

When only $S_1$ is closed,
$R_{eq}=R+3R=4R$
$I=\frac{E}{R_{eq}}=\frac{E}{4R}$
Reading of the voltmeter $V_1=\frac{E}{4R}\times 3R=\frac{3E}{4}$

When only $S_2$ is closed,
$R_{eq}=R+6R=7R$
$I=\frac{E}{R_{eq}}=\frac{E}{7R}$
Reading of the voltmeter $V_2=\frac{E}{7R}\times 6R=\frac{6E}{7}$

When both $S_1$ and $S_2$ are closed,
$R_{eq}=R+\frac{3R\times 6R}{3R+6R}=R+2R=3R$
$I=\frac{E}{R_{eq}}=\frac{E}{3R}$
Reading of the voltmeter $V_3=\frac{E}{3R}\times 2R=\frac{2E}{3}$

Hence, $V_2>V_1>V_3$