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

by Northbysouth
Tags: aluminum, copper, diameter, equal, length, resistance, wire
 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.
HW Helper
PF Gold
P: 1,973
 Quote by 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? 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)