Problem 2.1  Source:   Problem developed by the author of the site.

Knowing that the copper resistivity is 1.69 x 10 ^-2 ohms. mm ² / m and that of aluminum is 2.75 x 10 ^-2 ohms. mm ² / m , what should be the relationship between the areas of the copper and aluminum to have the same resistance, considering the wires with the same length?

Solution of the Problem 2.1

As we should have equal resistance, then we can write:

As the problem says that we have to have equal lengths of the wires, then we can consider only the electrical conductivity and the area of each wire, thus:

Therefore, we conclude that the relationship between the areas depends only on the relationship between the electrical conductivity of the wires. Then:

From this result, we can conclude that for a copper wire of the same length as an aluminium, just have 61.45% of the area of the latter so that we have resistances equal.