Question

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

• A. $R_{1}$ is two times $R_{2}$
• B. $R_{2}$ is two times $R_{1}$
• C. $R_{2}$ is four times $R_{1}$
• D. $R_{1}$ is four times $R_{2}$

Answer 1

Answer: (B)

$R_{2}$ is two times $R_{1}$

Answer 2

$P \propto \frac{1}{R} \Rightarrow \frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}}$ $\Rightarrow \frac{200}{100} = \frac{R_{2}}{R_{1}} \Rightarrow R_{2} = 2R_{1}$