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

[Northbysouth]

Homework Statement

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

Homework Equations

R = ρL/A

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

ρ_Copper = 1.72x10^-8 Ωm
ρ_Aluminum = 2.82x10^-8 Ωm

The Attempt at a Solution

So I knew that R_copper = R_Aluminum

(1.72x10^-8Ωm)(L)/A_copper = (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.

 

[collinsmark]

Homework Statement

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

Homework Equations

R = ρL/A

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

ρ_Copper = 1.72x10^-8 Ωm
ρ_Aluminum = 2.82x10^-8 Ωm

The Attempt at a Solution

So I knew that R_copper = R_Aluminum

(1.72x10^-8Ωm)(L)/A_copper = (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]

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

A_copper = 7.4364x10^-6 m²

r_{copper wire} = sqrt(7.4363x10²/π)

Diameter of copper wire = 2r = 3.077059 mm

Thanks for your help