Final answer:
An aluminum wire must have a larger cross-sectional area than a copper wire to have the same conductivity, typically requiring a larger diameter due to aluminum's lower electrical conductivity.
Step-by-step explanation:
To have the same conductivity, an aluminum wire must be larger in cross-sectional area compared to a copper wire due to aluminum's lower electrical conductivity. When comparing wires of the same length and resistance, the aluminum wire would need to have a larger diameter to compensate for its lower conductivity. This is because the resistance of a wire is inversely proportional to its cross-sectional area (A = πd2/4 for a wire of diameter d). Because copper has a higher conductivity, a smaller diameter copper wire can have the same resistance as a larger diameter aluminum wire.
However, despite the need for a larger cross section, aluminum is often used in household wiring due to its lower cost. It's important to note that aluminum expands more with heat than copper, which can lead to loose connections, posing a fire hazard. Special care must be taken when making connections with aluminum wiring.