Two bulbs marked 220 V, 200 W and 220 V, 1000 W, respectively, are connected in series to 220 V mains supply. The ratio of heat generated in them, respectively will be

5:1

The correct answer is Option (2) → 5:1

Given:

Bulb A: 220 V, 200 W       Bulb B: 220 V, 1000 W

First, calculate the resistance of each bulb using the formula:

$R = \frac{V^2}{P}$

For Bulb A:

$R_1 = \frac{220^2}{200} = \frac{48400}{200} = 242\,\Omega$

For Bulb B:

$R_2 = \frac{220^2}{1000} = \frac{48400}{1000} = 48.4\,\Omega$

Since they are connected in series, the same current flows through both. Heat produced in time $t$ is given by:

$H = I^2 R t$

So, the ratio of heat generated is proportional to their resistances:

$\frac{H_1}{H_2} = \frac{R_1}{R_2} = \frac{242}{48.4} = 5:1$