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Specific Heat Capacity

In the follow...

Question

In the following figure, the reading of an ideal voltmeter $V$ is zero. Then, the relation between $R, r_{1}$ and $r_{2}$ is

A

R = r_{2} - r_{1}

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B

R = r_{1} - r_{2}

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C

R = r_{1} + r_{2}

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D

R = \frac{r_{1} r_{2}}{r_{2} + r_{1}}

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Solution

The correct option is B $R = r_{1} - r_{2}$
According to question
$V = 0$
$E - I_{r_{1}} = 0$
$I = \frac{E}{r_{1}}$
$∴ I = \frac{2 E}{R + r_{1} + r_{2}} = \frac{E}{r_{1}}$
$\Rightarrow 2 r_{1} = R + r_{1} + r_{2}$
$R = r_{1} - r_{2}$

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