A copper wire is stretched to make it 0.5 % longer. The percentage change in its electrical resistance if its volume remains unchanged is:

Question

A copper wire is stretched to make it 0.5 % longer. The percentage change in its electrical resistance if its volume remains unchanged is: (A) 2.5 % (B) 0.5 % (C) 1.0 % (D) 2.0 %

Tardigrade Admin · Accepted Answer

R = (ρℓ/A) and volume (V) = Aℓ. R = (ρℓ2/V) ⇒ (Δ R/R) = (2Δℓ/ℓ) = 1 %

Q. A copper wire is stretched to make it $0.5%$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:

2.5 %

0.5 %

1.0 %

2.0 %

$R = \frac{ρ ℓ}{A}$ and volume (V) = A $ℓ$ .
$R = \frac{ρ ℓ ^{2}}{V}$
$\Rightarrow \frac{Δ R}{R} = \frac{2Δ ℓ}{ℓ} = 1%$

Q. A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is: