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 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. $V_{1} >\, V_{2} >\, V_{3}$

Answer 1

Answer: (B)

In series, p.d. $\propto R$
When only $S_{1}$ is closed, $V_{1}=\frac{3}{4} \varepsilon=0.75 \varepsilon$
When only $S_{2}$ is closed, $V_{2}=\frac{6}{7} \varepsilon=0.86 \varepsilon$
When both $S_{1}$ and $S_{2}$ are closed combined resistance of $6R$ and $3 R$ is $2 R$.
$\therefore V_{3}=\left(\frac{2}{3}\right) \varepsilon=0.67 \varepsilon$
$\therefore V_{2} >\,V_{1} >\, V_{3}$