Question

If $R_1$ and $R_2$ are respectively the filament resistance of a $200W$ bulb and $100W$ 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

The correct option is B $R_2$ is two times $R_1$

Given :

$P_1=200$ W

$P_2=100$ W

Power, voltage and resistance are related as

$P=\frac{V^2}{R}\Rightarrow R=\frac{V^2}{P}$

For constant voltage,

$⟹$ $R\propto \frac{1}{P}$

$\therefore$ $\frac{R_1}{R_2}=\frac{P_2}{P_1}=\frac{100}{200}$ $⟹R_2=2R_1$