Question

In the circuit shown in figure when $S_1$ is closed and $S_2$ is open, the ideal voltmeter shown a reading 18 V. When switch $S_2$ is closed and $S_1$ is open, the reading of the 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. None of these

Answer 1

The correct option is A 14.4 V

Hello Amal, let r be the internal resistance of the cell and E is the e m f of the source

So $V\ast (r+R)=R\ast E$

Now in first case $R=6$ ohm and $V=18V$

Second case $R=12$ ohm and $V=24V$

So $18\ast (r+6)=6\ast E$ --(1)

And $24\ast (r+12)=12\ast E$ --(2)

Dividing (2) by (1) we get, $4/3\ast (r+12)/(r+6)=2$

$===>2(r+12)=3\ast (r+6)$

Or r = 6 ohm

Now we can find E as 36 V

So when both switches closed then equivalent resistance will be $6\ast 12/(6+12)=4ohm$

Hence the voltmeter reading will be got from $ER=V(r+R)$

$===>36\ast 4=V(6+4)$

Hence V = 14.4 V