Question

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

• A. Between $81W$ and $90W$
• B. $81W$
• C. $90W$
• D. Between $90W$ and $100W$

Answer 1

The correct option is A Between $81W$ and $90W$

Let the initial resistance of the lamp filament be $R.$
Given $P=100WV=220V,$
We know that
$P=\frac{V^2}{R}$
then
$100=\frac{(220{)}^2}{R}$
$R=\frac{{220}^2}{100}=484\Omega$
When voltage drop $10\%,$ the final voltage $V^{\prime }=220-\frac{220}{10}=198V$
Now the expected power
$P=\frac{V^{\prime 2}}{R}=\frac{{198}^2}{484}=81W$
Suppose now resistance is $R^{\prime }$
So power
$P^{\prime }=\frac{(198{)}^2}{R^{\prime }}$
Here $R^{\prime }$ Will be less than $R,$ because now the rise in temperature will be less so the rise in Resistance will also be less
Therefore $P^{\prime }$ is more than $81W$
But it will not be $90\%$ of the earlier value because the fall in temperature is small.
Hence, option $\left(d\right)$ is correct.