Question

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

• A. $R_1=2R_2$
• B. $R_2=2R_1$
• C. $R_2=4R_1$
• D. $R_1=4R_2$

Answer 1

The correct option is B $R_2=2R_1$

Given that,

Power of bulbs $P_1=200W{P}_2=100W$

The power $P=VI$, and $I=V/R$

On substituting we get, $P=\frac{V^2}{R}$.

Here, the power $P_1$ used in case of $R_1$ is $P_1=\frac{V^2}{R_1}=200W$..........(1)

The power $P_2$ used in case of $R_2$ is $P_2=\frac{V^2}{R_2}=100W$.........(2)

On taking ration,

$\frac{P_1}{P_2}=\frac{R_2}{R_1}=\frac{200}{100}$.

Hence, $R_2=2R_1$.

Option B