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College Physics

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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.

  • College Physics -

    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%

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