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?

Answer 1

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