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  4. 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

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Q. 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

BHUBHU 2010Electromagnetic Induction

Solution:

Let the resistance of the lamp filament be $R$.
Then, $100=(220)^{2} / R$.
When the voltage drops, expected power is
$P=(220 \times 0.9)^{2} / R^{'}$
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.