Question

If voltage across a bulb rated \(220\,V, 50\,W\) drops by \(5\%\) of its rated value, the percentage of the rated value by which the power would decrease is

• A. \(10\%\)
• B. \(2.5\%\)
• C. \(15\%\)
• D. \(5\%\)

Hint:

Power varies as square of voltage, so small change in voltage causes double percentage change in power (approx).

Answer 1

The Correct Option is A

Step 1: Power relation.
\[ P = \frac{V^2}{R} \]

Step 2: Voltage decreases by 5%.
\[ V' = 0.95V \]

Step 3: New power.
\[ P' = \frac{(0.95V)^2}{R} \]
\[ P' = 0.9025 P \]

Step 4: Percentage decrease.
\[ \text{Decrease} = (1 - 0.9025)\times 100 \]

Step 5: Calculate.
\[ = 9.75\% \approx 10\% \]

Step 6: Final conclusion.
\[ \boxed{10\%} \] Hence, correct answer is option (A).