Question

The resistance of the filament of a lamp increases with the increase in temperature. A lamp rated 100 W and 220 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 100W
• D. between 81 and 90W

Answer 1

Answer: (D)

Let the resistance of the lamp filament be $R$.
Then, $100=(220{)}^2/R$.
When the voltage drops, expected power is
$P=(220\times 0.9{)}^2/R^{{}^{\prime }}$
Here, $R^{\prime }$ will be less than $R$, because now the rise in temperature will be less.
Therefore, $P$ is more than $(220\times 0.9{)}^2/R=81W$.
But it will not be $90\%$ of earlier value, because fall in temperature is small.