Answer to Question #327128 in Physics for grey tyrant

Question #327128

A wire with a resistance of 5Ω is drawn out through a die so that its new length is four times its original length. What is the resistance of the longer wire when the resistivity and density of the material are unchanged?


1
Expert's answer
2022-04-11T12:44:22-0400
R=ρlAR=\rho \frac{l}{A}

The density of the wire remains the same, hence the volume of the wire would be unchanged

V=lA=constV=lA=const

The new resistance of the wire

R=ρlA=ρ4lA/4=16R=165Ω=80ΩR'=\rho'\frac{l'}{A'}=\rho\frac{4l}{A/4}=16R\\ =16*5\:\Omega=80\:\Omega


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