Question

In the given circuit the internal resistance of the $18V$ cell is negligible. If $R_1=400\Omega ,R_3=100\Omega$ and $R_4=500\Omega$ and the reading of an ideal voltmeter across $R_4$ is $5V$, then the value of $R_2$ (in $\Omega$) will be:

Answer 1

Answer: 300

Across $R_4$ reading of voltmeter, $V_4=5V$
Current, $i_4=\frac{V_4}{R_4}=0.01A$
$V_3=i_1{R}_3=1V$
$V_3+V_4=6V=V_2$
$V_1+V_3+V_4=18V$
$\Rightarrow V_1=12V$
$i=\frac{V_1}{R_1}=0.03A$
$i=i_1+i_2$
$\Rightarrow i_2=i-i,=0.03-0.01A=0.02A$
$\therefore R_2=\frac{V}{i_2}=\frac{6}{0.02}=300\Omega$