Two bulbs A and B are rated 100W and 25W, respectively, at a given voltage. The ratio of resistance of bulb A to that of bulb B is:

Correct option is C

Correct Answer: (C) 1:4

Explanation:

The resistance R of a bulb is given by the formula:

​$$R= \frac{V^2}{P}$$​​

Where:

• V is the voltage,
• P is the power rating.

Let R_A and R_B​ be the resistances of bulbs A and B, respectively.

Step 1: Calculate the ratio of resistances.

​$$\frac{R_A}{R_B} = \frac{\frac{V^2}{P_A}}{\frac{V^2}{P_B}} = \frac{P_B}{P_A}$$​​

Given:

• PA=100W,
• PB=25W.

​$$\frac{R_A}{R_B} = \frac{25}{100} = \frac{1}{4}$$​​

Thus, the ratio of resistance of bulb A to that of bulb B is 1:4.