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## Homework Statement

A long round wire of radius

*a*and conductivity

*σ*is coated with a material of conductivity 0.1

*σ*. (a) What must be the thickness of the coating so that the resistance per unit length of the uncoated wire is reduced by 50%?

2. Homework Equations [/B]

R = l/(

*σS)*

where R is the resistance, l is the length of the wire,where R is the resistance, l is the length of the wire,

*σ*the conductivity and S the cross sectional area## The Attempt at a Solution

regarding part a) the resistance per unit length of the uncoated wire is (

*1/σS) this equals 1/(**σπa*^{2}meaning that its resistance per unit length doesn't depend on the thickness of the coating.

However the soln manual

solved it by setting: resistance per unit length of coated wire = resistance per unit length of uncoated wire

Why is that so??