Question

Aluminum wiring was used in many homes in the 1960s due to the high cost of copper at the time. Aluminum wire that was 12 gauge (a measure of cross-sectional area) was rated at 15 A of current. If copper wire of the same gauge were used to replace the aluminum wire, what current should the wire be capable of carrying if all factors except resistivity are considered equal? Assume that the resistance of the wire is the primary factor that determines the current it can carry and the cross-sectional area and length are the same for the aluminum and copper wires.

Answer 1

The resistivity of aluminum is greater than that of copper, which means that aluminum has a higher resistance for a given wire length and cross-sectional area. To determine the current capacity of copper wire with the same gauge as aluminum wire, we can use the equation for resistance (R = ρ * L / A), where ρ is the resistivity, L is the length, and A is the cross-sectional area.

Since the cross-sectional area and length are the same for both wires, we can compare their resistivities and calculate the ratio of their resistances. The resistivity of aluminum is about three times that of copper, so the resistance of the aluminum wire will be three times greater than the resistance of the copper wire.

Therefore, the current capacity of the copper wire, given all factors except resistivity are equal, will be three times greater than the current capacity of the aluminum wire. If the aluminum wire was rated at 15 A of current, then the copper wire should be capable of carrying 15 * 3 = 45 A of current.