Question

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

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

Answer 1

The correct option is D between $81W$ and $90W$

Using $P=\frac{V^2}{R}$, the resistance of filament of lamp is

$R=\frac{{220}^2}{100}=484\Omega$

When voltage drop 10 %, the final voltage $V^{\prime }=220-\frac{220}{10}=198V$

Now the expected power $P=\frac{V^{\prime 2}}{R}=\frac{{198}^2}{484}=81W$

Due to voltage drop temperature rise will be less, so the resistance will be less than from previous. Thus, the power will be more than 81 W. But it will not be 90% of the earlier value, because fall in temperature is small. Hence, option (d) is correct.