In the circuit shown in the figure, the ammeter reads 5 A and the voltmeter reads 250 V. If the resistance of the voltmeter is \( 2500\,\Omega \), the value of R is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 51\,\Omega \)
The figure shows the ammeter in the main line and the voltmeter connected across R. The voltmeter reads the potential difference across R. But it also draws a current of its own. So the ammeter current divides between R and the voltmeter.
The current through the voltmeter is:
\( \begin{aligned} I_V &= \frac{V}{R_V} \\ &= \frac{250\,\mathrm{V}}{2500\,\Omega} \\ &= 0.1\,\mathrm{A} \end{aligned} \)
The current through R is:
\( \begin{aligned} I_R &= I-I_V \\ &= 5\,\mathrm{A}-0.1\,\mathrm{A} \\ &= 4.9\,\mathrm{A} \end{aligned} \)
The resistance is then:
\( \begin{aligned} R &= \frac{V}{I_R} \\ &= \frac{250\,\mathrm{V}}{4.9\,\mathrm{A}} \\ &\approx 51\,\Omega \end{aligned} \)