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A wire of initial length L0 and radius r0 has a measured resistance of 2.5 . The wire is drawn under tensile stress to a new uniform radius of r = 0.45r0. What is the new resistance of the wire?

  • physics -

    Rₒ=2.5 Ω (units?) , Lₒ, rₒ,
    r=0.45•rₒ.
    R =?

    The wire volume stays constant
    V= Aₒ•Lₒ = A•L => Lₒ/L =A/Aₒ.
    Rₒ=ρ•Lₒ/Aₒ,
    R=ρ•L/A,
    Rₒ/R = Lₒ•A/L•Aₒ=
    =(Lₒ/L) •(A/Aₒ)=
    =(A/Aₒ)²= (π•r²/π•rₒ²)²=
    =(0.45•rₒ/rₒ)^4=0.041.
    R=Rₒ/0.041 = 2.5/0.041=61 Ω

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