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Types of Electric Circuits Series and Parallel

Two resistanc...

Question

Two resistances $R_{1}$ and $R_{2}$ when connected in series consume power equal to $25 W$ . When connected in parallel they consume $100 W$ . The ratio of power of each is.

A

\frac{1}{4}

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B

\frac{1}{3}

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C

\frac{1}{2}

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D

1

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Solution

The correct option is C $1$
$P_{R_{1}} + P_{R_{2}} = 25 P_{R_{1}} + P_{R_{2}} = 100$

$I^{2} [R_{1} + R_{2}] = 25 E^{2} [\frac{1}{R_{1}} + \frac{1}{R_{2}}] = 100$

$\frac{E^{2}}{(R_{1} + R_{2})} = 25$

$\Rightarrow 25 (R_{1} + R_{2})^{2} = 100 R_{1} R_{2}$

$\Rightarrow (R_{1} - R_{2})^{2} = 0$

$R_{1} = R_{2}$

$\frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}} = 1$

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