Question

If $R_1$ and $R_2$ are respectively the filament resistances of a $200watt$ bulb and a $100watt$ bulb designed to operate on the same voltage

• 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 $R_1$

$R_1=\frac{V^2}{P_1}$ and $R_2=\frac{V^2}{P_2}$

because both are operating same voltage that;s why resistance will directly depend upon power of filaments.

$\therefore \frac{R_2}{R_1}=\frac{P_1}{P_2}=\frac{200}{100}=2$ $(\because V=$ constant$)$

$R_2=2R_1$