Question

In the circuit shown in 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. The reading of voltmeter is $V_3$, when both $S_1$ and $S_2$ are closed, then

• 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 $S_1$ is closed


Applying KVL
$-E+3IR+IR=0$
$I=\frac{E}{4R}$

From $V=IR$
$V_1=\left(\frac{E}{4R}\right)3R=\frac{3E}{4}=0.75E$

When $S_2$ is closed


Applying KVL
$-E+6IR+IR=0$
$I=\frac{E}{7R}$
$V_2=\left(\frac{E}{7R}\right)6R=\frac{6E}{7}=0.85E$

When both $S_1$ and $S_2$ are closed


As $6R,3R$ are in parallel, their effective resistance is $2R$
Applying KVL
$-E+2IR+IR=0$
$I=\frac{E}{3R}$
$V_3=\frac{E}{3R}\times 2R=\frac{2E}{3}=0.66E$


$\Rightarrow V_2>V_1>V_3$