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Ohm's Law in Scalar Form

If R1 and ...

Question

If $R_{1}$ and $R_{2}$ are, respectively the filament resistance of a 200 watt bulb and a 100 watt bulb designed to operated on the same voltage.

A

R_{1}

is two times

R_{2}

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B

R_{2}

is two times

R_{1}

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C

R_{2}

is four times

R_{1}

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D

R_{1}

is four times

R_{2}

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Solution

The correct option is A $R_{2}$ is two times $R_{1}$
Power of bulb is inversely proportional to the resistance of filament wire of bulb hence,
$\frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}}$

$\frac{200}{100} = \frac{R_{2}}{R_{1}}$

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

Hence, $R_{2} = 2 R_{1}$

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