Final answer:
Aluminum conductors require a larger diameter than copper to achieve the same resistance per unit length due to its higher resistivity, despite being more cost-effective. They also have concerns such as oxidation and thermal expansion which can affect connections and demand careful use.
Step-by-step explanation:
For the same size of conductor, aluminum conductors have a lower ampacity than do copper conductors. Aluminum requires a larger diameter to match the resistance per length of copper wires because it has a higher resistivity. Despite its lower cost compared to copper, aluminum has some drawbacks, such as its propensity to oxidize which does not conduct electricity and can lead to connection problems. Additionally, aluminum has a higher rate of thermal expansion which can cause connections to loosen over time, potentially leading to a fire hazard. Special techniques and components designed for aluminum must be used to mitigate these issues.
To find the ratio of the diameter of aluminum to copper wire if they have the same resistance per unit length, we must consider that the resistivity of aluminum is higher than that of copper. Therefore, for aluminum and copper wires of the same length to have the same resistance, the aluminum wire would need to have a larger diameter. This compensates for the higher resistivity, allowing the wire to carry a similar current as a copper wire with the same resistance levels.