JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Current Electricity

If a copper wire is stretched to increase its length by

20%

. The percentage increase in resistance of the wire is ______ %.

Answer: 44

Solution

When a wire is stretched its volume stays fixed, so with

R = ρ \frac{L}{A}

and

A \propto \frac{1}{L}

the resistance varies as

R \propto L^{2}

. A

20%

longer wire has

L = 1.2 L_{0}

, so

\frac{Δ R}{R _{0}} = (1.2)^{2} - 1 = 1.44 - 1 = 0.44

. The resistance increases by

44%

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Integer answer