First slide

Electrical power

Question

A potential difference V is applied across a resistor of resistance R. If the voltage across the resistor increases by 1% and the resistance increases by 2%, then the maximum possible change in the power dissipated in the resistor is

Moderate

A

4%
B

3%
C

2%
D

5%

Solution

$P = \frac{V^{2}}{R} = V^{2} R^{- 1} \Rightarrow {(\frac{Δ P}{P})}_{\max} \times 100 % = 2 (\frac{Δ V}{V}) \times 100 % + (\frac{Δ R}{R}) \times 100 %$
$∴ {(\frac{Δ P}{P})}_{\max} \times 100 % = 2 \times 1 % + 2 % = 4 %$

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