Question

A wire P has resistance R. If the wire is stretched and its length is increased by 10%, what would be the percentage change in its resistance? (Assume the density of the wire remains constant)

A) - 10%
B) 0 %
C) 10%
D) 20%


My thoughts:
Since resistance is R = resistivity x length / cross-sectional area of wire, when the length increases by 10%, R should increase by 10%. Cross sectional area doesn't change as the wire is stretched, as the atoms are horizontally pulled apart in the direction of the stretch and have a wider spacing between each other.

However, the answer given is D.

Answer 1

Since the density stays the same, the volume (area*length) must stay the same and the cross sectional area must decrease.

Resistance = Resisitivity*Length/Area
(new resistance)/(old resistance)
= [(new length)/(old length)]*(old area)/(new area)]
= 1.1/(1/1.1) = 1.21

The increase is acually 21%, not 20%