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

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 %

Tardigrade Admin · Accepted Answer

Power, P=(V2/R) As the resistance of the bulb is constant ∴ (Δ P/P)=(2 Δ V/V) % decrease in power =(Δ P/P) × 100 =(2 Δ V/V) × 100 =2 × 2.5 %=5 %

Q. 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

$20 %$

$2.5 %$

$5 %$

$10 %$

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

Q. If 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

20%

2.5%

5%

10%