Some states allow the use of aluminum wire in houses in place of copper. If you wanted the resistance of your aluminum wire to be the same as that of copper, would the aluminum wire have to have a greater diameter than, smaller diameter than, of the same diameter as the copper wire? Calculate the thickness ratio of aluminum to that of copper.
Are you using 12 volt batteries to do this..?
The resistivity of copper is ρ_Cu = 1.72 x 10^(-8) ohm - meters, whereas that of aluminum is ρ_Al = 2.82 x 10^(-8) ohm-meters [1]. Assuming that the wire runs are the same length L, the resistance in the aluminum wire will be R_Al = ρ_Al * L/A_Al, where A_Al is the cross-sectional area of the aluminum wire. The resistance in the copper wire will be R_Cu = ρ_Cu * L/A_Cu. If we want the same resistance in both wires, we require R_Cu = R_Al: ρ_Cu * L / A_Cu = ρ_Al * L / A_Al A_Al / A_Cu = ρ_Al / ρ_Cu. Since the resistivity ρ_Al of aluminum is higher, the aluminum wire must have a larger cross sectional area to yield the same resistance. To make this precise, suppose the wires are cylindrical. Then the cross sectional area is π(R_Al)? for the aluminum wire and π(ρ_Cu)? for the copper wire: π(R_Al)?/π(ρ_Cu)? = ρ_Al / ρ_Cu R_Al/R_Cu = √(ρ_Al / ρ_Cu) = √(2.82/1.72) = 1.28 The aluminum wire must be 28% thicker than the copper wire in order to provide the same resistance.
