A, B and C are voltmeters of resistance R, 1.5R and 3 R respectively as shown in the figure. When some potential difference is applied between X and Y, the voltmeter readings are $V_{A}, V_{B} and V_{C}$ respectively. Then

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$V_{A} \neq V_{B} \neq V_{C}$

$V_{A} = V_{B} = V_{C}$

$V_{A} = V_{B} \neq V_{C}$

$V_{A} \neq V_{B} = V_{C}$

answer is C.

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Detailed Solution

According to the fi gure,
voltmeters B and C are in parallel.
Potential difference across them will be
same.
V_b = V^c
Given, resistances of B and C are 1.5 R and 3 R.
Their effective resistance will be
$\begin{array}{l} R_{eff} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} \\ = \frac{1.5 R \times 3 R}{1.5 R + 3 R} \\ = R \end{array}$
The effective resistance of B and C is same as that of voltmeter A.
Since the resistance is same, there will be
equal drop in potential across A, B and C.
$\Rightarrow V_{A} = V_{B} = V_{C}$