Question

In the given circuit, the voltmeter records $5V$. The resistance (in $\Omega$ ) of the voltmeter is

Answer 1

Answer: 100

Let the resistance of voltmeter be $G\Omega$.
$\therefore$ Total resistance of the circuit, $R=\left(\frac{G\times 100}{G+100}+50\right)\Omega$
Total current, $i=\frac{V}{R}=\frac{10}{\left(\frac{G\times 100}{G+100}+50\right)}$
Voltage across $100\Omega$ resistance
$=i\left(\frac{G\times 100}{G+100}\right)=\frac{10}{\left(\frac{G\times 100}{G+100}+50\right)}\times \left(\frac{G\times 100}{G+100}\right)$
Reading of voltmeter $=5V$(Given)
$\therefore$ Voltage across $100\Omega =5V$
$\therefore 5=\frac{10}{\left(\frac{G\times 100}{G+100}+50\right)}\times \left(\frac{G\times 100}{G+100}\right)$
$\Rightarrow G=100\Omega$