Question

In the circuit shown, when switch $S_{1}$ is closed and $S_{2}$ is open, the ideal voltmeter shows a reading of $18\, V$. When switch $S_{2}$ is closed and $S_{1}$ is open, the reading of voltmeter is $24\, V$. When $S_{1}$ and $S_{2}$ both are closed, the voltmeter reading will be

• A. 14.4 V
• B. 20.6 V
• C. 24.2 V
• D. 10.8 V

Answer 1

Answer: (A)

Terminal potential difference across the terminals of cell $E$
$V=E-i r=E-\left(\frac{E}{r+R}\right) r=\frac{E R}{R+r}$
According to question,
$18=\frac{6 E}{6+r} ........ (i) $
and $24=\frac{12 E}{12+r} .........(ii) $
Solving (i) and (ii), we get $r=6\, \Omega, E=36\, V$
When both $S_{1}$ and $S_{2}$ are closed, the effective external resistance in the circuit will be,
$R=\frac{6 \times 12}{18}=4\, \Omega$
So, $V=\frac{E R}{r+R}=\frac{36 \times 4}{6+4}=\frac{144}{10}$
$V=14.4$ volt