Question

If the voltage across a bulb rated $220V-100W$ 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

The correct option is C $5\%$


Given ,$\frac{\Delta V}{V}\times 100=2.5$ %
$P=\frac{V^2}{R}$
Hence,
$\frac{\Delta P}{P}=2\times \frac{\Delta V}{V}$
using, $\frac{\Delta V}{V}\times 100=2.5$ %
$\frac{\Delta P}{P}\times 100=2\times 2.5$ = $5$%
Hence, option C is correct.