Search any question & find its solution
Question:
Answered & Verified by Expert
In the given circuit, the voltmeter records $5 \mathrm{~V}$. The resistance of the voltmeter (in ohms) is
Options:
Solution:
1823 Upvotes
Verified Answer
The correct answer is:
100
If $R$ be the resistance of voltmeter, then the equivalent resistance of circuit is
$\begin{aligned}
R_{e q} &=\frac{R \times 100}{100+R}+50 \\
&=\frac{150 R+5000}{R+100}
\end{aligned}$
Total current in circuit,
$i=\frac{V}{R_{\text {eq }}}=\frac{10}{\frac{150 R+5000}{(R+100)}}$
$=\frac{10(R+100)}{150 R+5000}$
Voltage across $100 \Omega$ resistor,
$V=i\left(\frac{R \times 100}{\underline{R}+100}\right)$
Given, $\quad V=5 \mathrm{~V}$
$\therefore \quad 5=\frac{10(R+100)}{150 R+5000} \times \frac{R \times 100}{R+100}$
$=\frac{1000 R}{150 R+5000}$
$\Rightarrow 750 R+25000=1000 R$
$\Rightarrow \quad R=100 \Omega$
$\begin{aligned}
R_{e q} &=\frac{R \times 100}{100+R}+50 \\
&=\frac{150 R+5000}{R+100}
\end{aligned}$
Total current in circuit,
$i=\frac{V}{R_{\text {eq }}}=\frac{10}{\frac{150 R+5000}{(R+100)}}$
$=\frac{10(R+100)}{150 R+5000}$
Voltage across $100 \Omega$ resistor,
$V=i\left(\frac{R \times 100}{\underline{R}+100}\right)$
Given, $\quad V=5 \mathrm{~V}$
$\therefore \quad 5=\frac{10(R+100)}{150 R+5000} \times \frac{R \times 100}{R+100}$
$=\frac{1000 R}{150 R+5000}$
$\Rightarrow 750 R+25000=1000 R$
$\Rightarrow \quad R=100 \Omega$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.