Two wires have the same resistance and diameter. if the wires are made of platinum and gold with resistivities respectively of 11.0 ✕ 10−8 ω · m and 2.44 ✕ 10−8 ω · m, determine the ratio of their lengths.

0.222

Explanation:

The resistance of a wire is given by

where

is the resistivity

L is the length of the wire

A is the cross-sectional area

Here let's call the resistance of the platinum wire and the resistance of the gold wire. The two resistances are equal, so we can write

Where

is the resistivity of platinum

is the resistivity of gold

We know that the two wires also have same diameter, so same cross-sectional area, so

Therefore we can rewrite the equation as

And so the ratio of the lengths of the two wires is