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Alternating Current Applied to an Inductor

Two electric ...

Question

Two electric bulbs, rated for the same voltage, have powers of 200 W and 100 W, respectively. If their resistances are $r_{1}$ and $r_{2}$ , respectively, then

A

r_{1} = 2 r_{2}

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B

r_{2} = 2 r_{1}

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C

r_{2} = 4 r_{1}

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D

r_{1} = 4 r_{2}

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Solution

The correct option is B $r_{2} = 2 r_{1}$
We know that power $P = \frac{V^{2}}{R}$
As $V$ is same for both bulb so:
$\frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}}$
$\frac{200}{100} = \frac{r_{2}}{r_{1}}$
$∴ r_{2} = 2 r_{1}$

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