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

by Northbysouth
Tags: aluminum, copper, diameter, equal, length, resistance, wire
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Northbysouth
#1
Oct2-12, 08:41 PM
P: 248
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?

Give your answer in mm


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.
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collinsmark
#2
Oct2-12, 09:39 PM
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Quote Quote by Northbysouth View Post
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?

Give your answer in mm


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)
Start with what I've highlighted above in red.
  • 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.]
Northbysouth
#3
Oct2-12, 09:57 PM
P: 248
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

Thanks for your help


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