JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Current Electricity

A copper wire is stretched to make it

0.5%

longer. The percentage change in its electric resistance if its volume remains unchanged is

Answer: (C)

Solution

Keep in mind that when a wire is stretched at constant volume both its length and cross-section change, so write the resistance as

R = \frac{ρ ℓ}{A} = \frac{ρ ℓ ^{2}}{V}

using

V = A ℓ

. With the volume fixed,

R \propto ℓ^{2}

, and taking small changes gives

\frac{Δ R}{R} = 2 \frac{Δ ℓ}{ℓ}

. A

0.5%

increase in length therefore doubles into a

2 \times 0.5% = 1.0%

increase in resistance.

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option