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. $400\%$

Answer 1

The correct option is D $400\%$

Power $P=I^{2}R$
where, I is the current and R is the resustance.
Current is increased by $100\%$
New current = 2I
Resistance remains unchanged.
$P^{\prime }=(2I{)}^{2}R=4I^{2}R=4P$

percentage fractional change in power $\Delta P=\frac{P_f-P_i}{P_i}=\frac{4P-P}{P}\times 100=300\%$
$\therefore$ The increase in power dissipation will be $300\%$.