Question

As shown in the figure, the voltmeter reads 2V across 5Ω resistor. The resistance of the voltmeter is_____Ω.

Answer 1

Correct Answer: 20

Method-I: The equivalent resistance for the given circuit is: \[ R_{eq} = 2 + \frac{5R}{5 + R} \] Using Ohm's law: \[ i = \frac{3}{R_{eq}} = \frac{3}{5 + R} \] The current in the circuit is: \[ i = 3 \times \frac{5R}{5 + R} \] From the voltage readings, we calculate \(R = 20 \, \Omega\).
Method-II: Given potential across 5 \(\Omega\) and voltmeter is 2V, to find the resistance \(R\) of the voltmeter: \[ i = \frac{2}{5} = \frac{1}{2} \] Using junction law: \[ i = i_1 + i_2 \] Hence, \(R = 20 \, \Omega\).