Question

The resistance of the filament of a lamp increases with the increase in temperature. A lamp rated $100\text{W},220\text{V}$ is connected across $220\text{V}$ power supply. If the voltage drops by $10\%$ then the power of lamp will be

• A. $81\text{W}$
• B. $90\text{W}$
• C. Between $81\text{W}$ and $90\text{W}$
• D. Between $90\text{W}$ and $100\text{W}$

Answer 1

The correct option is C Between $81\text{W}$ and $90\text{W}$

Let the resistance of the lamp filament be $R$.
Then $100=\frac{(220{)}^2}{R}$.
When then voltage drops,
expected power is $P=\frac{(220\times 0.9{)}^2}{R^{\prime }}$.
Here $R\text{'}$ will be less than $R$, because the rise in temperature will be less.
Therefore $P$ is more than

$\frac{(220\times 0.9{)}^2}{R}=81\text{W}$

But it will not be $90\%$ of earlier value, because fall in temperature is small.
Hence, option $\left(D\right)$ is correct.