JEE Main · 2011 · 10 Apr 2011 · Offline · Current Electricity

If a wire is stretched to make it

0.1%

longer, its resistance will :

Answer: (A)

Solution

Resistance is

R = \frac{ρ ℓ}{A}

, and stretching keeps the volume

A ℓ

fixed, so the area falls as the length rises and

R \propto ℓ^{2}

. For a small change this means

\frac{Δ R}{R} = 2 \frac{Δ ℓ}{ℓ}

. A stretch of

0.1%

in length therefore raises the resistance by

2 \times 0.1% = 0.2%

, an increase.

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option