If the current I through a resistor is increased by 100%

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 $=\frac{P^{\prime}-P}{P} \times 100 \%$

$=300 \%$

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