Question

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

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Illumination of the lamp is the heat produced by lamp.

Thus, $H=I^{2}Rt\Rightarrow H\propto I^2$

so, $\frac{H_2}{H_1}=\frac{I_2}{I_1}$

here, $I_1=I$ and $I_2=I+I\times \left(20/100\right)=\left(6/5\right)I=1.2I$

$\frac{H_2}{H_1}=\frac{1.2I}{I}=1.2$

% of rise of illumination $=\frac{H_2-H_1}{H_1}\times 100=[\frac{H_2}{H_1}-1]\times 100=(1.44-1)100=44\%$

But there is 44% increase in illumination. So assertion is incorrect and reason is correct.