# Diameter of copper wire to have same resistance as equal length aluminum wire

1. Oct 2, 2012

### Northbysouth

1. The problem statement, all variables and given/known data
What diameter must a copper wire have if its resistance is to be the same as that of an equal length of aluminum wire with diameter 3.94mm?

2. Relevant equations

R = ρL/A

where A is the cross sectional area, L is the length and ρ resistance of the material

ρCopper = 1.72x10-8 Ωm
ρAluminum = 2.82x10-8 Ωm
3. The attempt at a solution

So I knew that Rcopper = RAluminum

(1.72x10-8Ωm)(L)/Acopper = (2.82x10-8Ωm)(L)/(0.00394m)

A = 0.00240 m
A = πr2

r = 0.027657 m

diameter = 55.31499 mm

But the system says its wrong and I don't see where I've gone wrong.

2. Oct 2, 2012

### collinsmark

• What are units for area: meters or square meters?
• Before calculating the cross section area of the copper wire, first ask, what is the cross sectional area of the aluminum wire?

[Edit: On a much lesser note, and I'm not sure if this matters, according to some sources I've looked at on the Internet, 1.72x10-8 Ωm is the resistivity of annealed copper. Plain old copper has a very similar resistivity, but slightly different. Use whatever your course material advises. And again, the difference is small and I'm not sure if copper vs. annealed copper matters.]

Last edited: Oct 2, 2012
3. Oct 2, 2012

### Northbysouth

I see what you're saying.

The cross section area od aluminum is π(0.00197m)2

3.8809x10-6 m2

Then solving for the cross sectional area of copper I get

Acopper = 7.4364x10-6 m2

rcopper wire = sqrt(7.4363x102/π)

Diameter of copper wire = 2r = 3.077059 mm