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Equivalent Resistance in Series Circuit

A, B and C ar...

Question

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

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

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

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

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

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Solution

The correct option is C $V_{A} = V_{B} = V_{C}$
As Resistance B and C are in parallel:
$V_{B} = V_{C}$
the equivalent resistance of resistor B and C $= \frac{R_{1} R_{2}}{R_{1} + R_{2}}$
$R_{e q} = (\frac{1.5 \times 3}{1.5 + 3}) \times R = R Ω$
as resistance A and $R_{e q}$ are equal, potential drop in each resistor will be equal.
$\Rightarrow V_{A} = V_{B} = V_{C}$
hence, correct answer is option C

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