Question

A closed circuit is shown in the figure. Voltage across $6\Omega$ is measured by voltmeter with resistance of $3\Omega$. Find the error in the reading.

• A. $10\%$
• B. $30\%$
• C. $50\%$
• D. $40\%$

Answer 1

The correct option is D $40\%$


$\%$ error $=\frac{V_{actual}-V_{measured}}{V_{actual}}\times 100$


$V_{actual}=$ Voltage across $6\Omega$ $=iR$
$=\left(\frac{45}{6+3}\right)6$
$=30\text{V}$

Current in the circuit
$i=\frac{45}{\frac{6\times 3}{6+3}+3}=\frac{45}{5}=9A$

Resistance across voltmeter $R^{\prime }=\frac{6\times 3}{6+3}=2\Omega$

Thus, $V_{measured}=i{R}^{\prime }=9\times 2=18\text{V}$

%error $=\frac{30-18}{30}\times 100$
$=40\%$