Q. The resistance of the filament of a lamp increases with the increase in temperature. A lamp rated 100 W and 200 V is connected across 220 V power supply. If the voltage drops by 10%, then the power of the lamp will be
A) 90 W
B) 81 W
C) Between 90 and 100 W
D) Between 81 and 90 W
Explanation
(d) Let the resistance of the lamp filament be $R.$ Then $100 = (220)^{2}/R.$ When the voltage drops, expected power is
$P = (220\ \times 0.3)^{2}/R'$
Here, $R'$ will be less than $R,$ because now the rise in temperature will be less. Therefore, $P$ is more than $(220\ \times 0.9)^{2}\ R = 81\ W.$ But it will not be 90% of earlier value, because fall in temperature is small. Hence, option (d) is correct.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.