Question

Assertion : If the current of a lamp decreases by 20%, the percentage decrease in the illumination of the lamp is 40%.
Reason : Illumination of the lamp is directly proportional to square of the current through lamp.

• A. Both (A) and (R) are true and (R) is the correct explanation of A.
• B. Both (A) and (R) are true but (R) is not the correct explanation of A.
• C. (A) is true but (R) is false
• D. (A) is false but (R) is true

Answer 1

The correct option is D (A) is false but (R) is true

$P=i^{2}R$

$\Rightarrow \frac{\Delta P}{P}=\frac{2\Delta i}{i}$ [Keeping R constant]
let the initial current be i

$\Rightarrow P_1=i^{2}R.$

final $i=08i$

$\Rightarrow P_2=0.64i^{2}R$
$\Rightarrow P_2=0.64P_1$

$\therefore$ % decrease of power $=$ 36 %