The figure shows three circuits I, II and III which are connected to a $3 V$ battery. If the powers dissipated by the configurations $I, I I$ and $I I I$ are $P_{1}, P_{2}$ and $P_{3}$ respectively, then :

P_{1} > P_{3} > P_{2}

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P_{2} > P_{1} > P_{3}

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P_{1} > P_{2} > P_{3}

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P_{3} > P_{2} > P_{1}

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Solution

The correct option is A $P_{2} > P_{1} > P_{3}$
It is a wheatstone bridge and current through 2-3 will be zero.
Equivalent resistance $= 2 R ∥ 2 R$
$\Rightarrow R_{e q} = R$
$\Rightarrow P_{1} = \frac{V^{2}}{R}$

For (II)

$\Rightarrow R_{e q} = 2 R ∥ R ∥ 2 R$
$\Rightarrow R_{e q} = \frac{2 R . R .2 R}{2 R^{2} + 2 R^{2} + 4 R^{2}}$
$\Rightarrow R_{e q} = \frac{R}{2}$
$\Rightarrow P_{2} = \frac{2 V^{2}}{R}$

For (III)

$\Rightarrow R_{e q} = 2 R ∥ 2 R + R = 2 R$
$\Rightarrow P_{3} = \frac{V^{2}}{2 R}$
$P_{2} > P_{1} > P_{3}$

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