First slide

Electrical power

Question

When a current of 2A flows through a metallic wire of radius 1 mm, rate of heat generation is 24 watt. What will be the rate of heat generation when 5 A current flows through a metallic wire made of same material and having same length and radius 2 mm?

Moderate

A

75 Watt
B

50 Watt
C

100 Watt
D

125 Watt

Solution

$P \propto i^{2} / r^{2} \Rightarrow \frac{P^{1}}{P} = {(\frac{i^{1}}{i})}^{2} {(\frac{r}{r^{1}})}^{2} = {(\frac{5}{2})}^{2} {(\frac{1}{2})}^{2} = \frac{25}{8} \Rightarrow P^{1} = \frac{25}{8} \times 24 W = 75 W$

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