First slide

voltmeter

Question

In the given circuit, the voltmeter records 5 volt. The resistance of the voltmeter in ohms is

Moderate

A

700
B

100
C

18
D

30

Solution

Let R be the resistance of voltmeter as shown in fig
The resultant ,resistance of the circuit
$\begin{array}{l} R_{resultant} = (\frac{R \times 100}{R + 100}) + 50 \\ = \frac{R \times 100 + 50 \times (R + 100)}{(R + 100)} \\ = \frac{150 R + 5000}{(R + 10^{'} 0)} \end{array}$
The current flowing ir.t the circuit
$i = \frac{10 V}{[(150 R + 5000)} \frac{}{' (R + 100)]}$
The voltage across AB, i.e., V' is given by $V^{'} = i \times R_{AB}$
$\begin{array}{l} = \frac{10}{[(150 R + 5000) / (R + 100)]} \times [\frac{R \times 100}{R + 100}] \\ 5 = [\frac{10}{150 R + 5000}] \times (R \times 100) \end{array}$
Solving, we get R = 100 $Ω$

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