Question

A $100-W$ bulb and a $25-W$ bulb are designed for the same voltage. They have filaments of the same length and material. The ratio of the diameter of the $100-W$ bulb to that of the $25-W$ bulb is

• A. $4:1$
• B. $2:1$
• C. $\sqrt{2}$ : 1
• D. $1:2$

Answer 1

The correct option is B $2:1$

We know that, $\frac{R_1}{R_2}=\frac{\left(\frac{V^2}{P_1}\right)}{\left(\frac{V^2}{P_2}\right)}=\frac{P_2}{P_1}$

$\frac{R_1}{R_2}=\frac{\frac{\rho l}{\pi (d_1/2{)}^2}}{\frac{\rho l}{\pi (d_2/2{)}^2}}=\frac{d_2^2}{d_1^2}=\frac{100W}{25W}$

$\Rightarrow \frac{d_2}{d_1}=\frac{10}{5}=\frac{2}{1}$