Question

If voltage across a bulb rated $220 \,V$- $100\, W$ drops by $2.5\%$ of its rated value, the percentage of the rated value by which the power would decrease is

• A. $20\,\%$
• B. $2.5\,\%$
• C. $5\,\%$
• D. $10\,\%$

Answer 1

Answer: (C)

Power, $P=\frac{V^{2}}{R}$
As the resistance of the bulb is constant
$\therefore \frac{\Delta P}{P}=\frac{2 \Delta V}{V}$
$\%$ decrease in power $=\frac{\Delta P}{P} \times 100$
$=\frac{2 \Delta V}{V} \times 100 $
$=2 \times 2.5 \%=5 \%$