Question

If the current through a resistor in a circuit increases by 3% , the power dissipated by the resistor

• A. Increases approximately by 3%.
• B. Increases approximately by 6%.
• C. Increases approximately by 9%.
• D. Decreases approximately by 3%.

Answer 1

Answer: (B)

Increases approximately by 6%.

Power $P=i^{2}R$ i - current and R-resistor.
Taking log on both sides,
$\log P=2\log i+\log R$
Differential form
$\frac{dP}{P}=2\frac{di}{i}+\frac{dR}{R}$
Keeping resistance unchanged if $\frac{di}{i}=3\%$
Then $\frac{dP}{P}=2\frac{di}{i}=6\%$