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Question

Question: If \(R_{1}\) and \(R_{2}\) are respectively the filament resistances of a 200 watt bulb and 100 watt...

If R1R_{1} and R2R_{2} are respectively the filament resistances of a 200 watt bulb and 100 watt bulb designed to operate on the same voltage, then

A

R1R_{1} is two times R2R_{2}

B

R2R_{2} is two times R1R_{1}

C

R2R_{2} is four times R1R_{1}

D

R1R_{1} is four times R2R_{2}

Answer

R2R_{2} is two times R1R_{1}

Explanation

Solution

P1RP1P2=R2R1P \propto \frac{1}{R} \Rightarrow \frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}} 200100=R2R1R2=2R1\Rightarrow \frac{200}{100} = \frac{R_{2}}{R_{1}} \Rightarrow R_{2} = 2R_{1}