Question

In the circuit shown in the figure when switch $S_1$ is closed and $S_2$ is open, the ideal voltmeter shows a reading $18V$. When switch $S_2$ is closed and $S_1$ is open, the reading of the voltmeter is $24V$. When $S_1$ and $S_2$ both are closed the voltmeter reading will be

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

Answer 1

The correct option is A $14.4V$

$\begin{array}{c}Theinternalresis\tan ceofthecellandEisthee.m.fofthesource\\ so,V\times \left(r+R\right)=RE\\ NowinfirstcaseR=6\Omega andV=18V\\ \sec ondcaseR=12\Omega andV=24V\\ So,18\times \left(r+6\right)=6\times E..........\left(1\right)\\ And24\times \left(r+12\right)=12\times E........\left(2\right)\\ \Rightarrow 2\left(r+12\right)=3\times \left(r+6\right)\\ or,r=6\Omega \\ NowwegetE=36V\\ sowhenbothswitchesclosedthenequivalentresis\tan cewillbe\frac{6\times 12}{\left(6+12\right)}=4\Omega \\ HencethevoltmeterreadingwillbegotfromER=V\left(r+R\right)\\ \Rightarrow 36\times 4=V\left(6+4\right)\\ Hence,\\ V=14.4V\end{array}$