A 1-m copper wire with a radius of 0.5 mm is stretched to a distance of 2 m.What is the fractional change in resistance $\Delta$R/R as the wire is stretched?
A)1.0
B)2.5
C)3.0
D)4.3
E)5.4

Question

Quizplus · Accepted Answer

The fractional change in resistance due to stretching, ∆R/R is given by:
∆R/R = (ρ/AL)(∆L/L)
Where ρ is the resistivity of copper, A is the cross-sectional area of the wire, L is the original length of the wire, and ∆L is the change in length of the wire. 
Substituting the given values, we get:
∆R/R = (ρ/πr2)(∆L/L) = (1.72 x 10^-8 Ωm)/(π(0.0005 m)2)(1 m) = 0.036
Therefore, the fractional change in resistance is 3.6%, which is closest to choice C) 3.0.

A 1-M Copper Wire with a Radius of 0 Δ\DeltaΔ R/R as the Wire Is Stretched? A)1

A 1-M Copper Wire with a Radius of 0 $\Delta$ R/R as the Wire Is Stretched?
A)1