Question

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

Answer: (B)

$R_2=2R_1$

The answer is B.

The power P = VI, substituitng I=V/R we get, $P=\frac{V^2}{R}$.
Here, the power P1 used in case of R1 is $P1=\frac{V^2}{R1}=200W$.
The power P2 used in case of R2 is $P2=\frac{V^2}{R2}=100W$.
$\frac{P1}{P2}=\frac{R1}{R2}=\frac{1}{2}$.
Hence, R2 = 2R1.