Question:
If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be
(a) 100 %
(b) 200%
(c) 300%
(d) 400%
Solution:
(c).
Explanation: Power dissipated, $\mathrm{P}=\mathrm{I}^{2} \mathrm{R}$
When $\mathrm{I}^{\prime}=\mathrm{I}+100 \%$ of $\mathrm{I}=2 \mathrm{I}$
Power dissipated, $\mathrm{P}^{\prime}=(2 \mathrm{I})^{2} \mathrm{R}=4 \mathrm{I}^{2} \mathrm{R}$
$\therefore$ Increase in power dissipated $=\frac{P^{\prime}-P}{P} \times 100 \%$
$=300 \%$