Problem 73-2  Source:   Problem developed by the author of the site.

Knowing that the resistivity of copper is 1.7241 x 10^-2 ohms.mm² /m and that of aluminum is 2.8264 x 10^-2 ohms.mm² /m , what should be the relation between the areas of copper wire and aluminum so that they have the same strength, considering the wires of the same length?

Solution of the Problema 73-2

As we must have equal resistances, then we can write:

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

Therefore, we conclude that the relation between the areas depends only on the relation between the electrical conductivity of the wires, ie:

Substituting for the numerical values we find:

From this result, we can conclude that for a copper wire of the same length than an aluminum one, just have 61% of the latter's area to have equal resistances.