Question

The coil of an electric bulb takes 40 watts to start glowing. If more than 40 W are supplied, 60% of the extra power is converted into light and the remaining into heat. The bulb consumes 100 W at 220 V. Find the percentage drop in the light intensity at a point if the supply voltage changes from 220 V to 200 V.

Answer 1

Case-I : When the supply voltage is 220 V.
Power consumed by the bulb = 100 W
Excess power = 100 − 40 = 60 W
Power converted to light = 60% of 60 W = 36 W

Case-II : When the supply voltage is 200 V.
Power consumed = $\frac{200}{220}\times 100$ = 82.64 W
Excess power = 82.64 − 40 = 42.64 W
Power converted to light = 60% of 42.64 W = 25.584 W

Percentage drop in light intensity,
$$\begin{gathered} p=\frac{36-25.584}{36}\times 100 \\ \Rightarrow p=28.93\approx 29\% \end{gathered}$$