Posted by **andrew** on Monday, May 21, 2012 at 3:14am.

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 -
**Elena**, Monday, May 21, 2012 at 4:13am
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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