By what percentage will the illumination of the lamp decrease if the current drops by 20%?

Solution

Physics sir · 4 steps

Brightness follows power, and power goes as current squared, so square the 0.8 before you subtract.

1. Link brightness. The illumination of a lamp is proportional to the power it uses. The filament resistance R is taken as constant, so P = I² R and P ∝ I².
2. New current. A 20% drop leaves I' = 0.8 I.

   P'/P = (I'/I)² = (0.8)² = 0.64

3. Percentage change. The new power is 64% of the old, so it falls by 100% - 64% = 36%.
4. So. The illumination decreases by 36%, which is option (b).

The idea to keep. When a quantity goes as the square of another, never scale the percentage directly. Write the multiplying factor (0.8), square it (0.64), then convert back to a percentage.

Answer from the NTA final answer key. Solution by PrepWiser.