A pail in a water well is hoisted by means of a frictionless winch, which consists of a spool and a hand crank. When Jill turns
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The resistance R of a piece of wire is given by
where
is the resistivity of the material, L is the length of the wire and A is its cross-sectional area.
Using this formula, and labeling with A the aluminum and with T the tungsten wire, we can write the ratio between
(the resistance of the tungsten wire) and 
(the resistance of the aluminum wire):
the two wires are identical, so L and A are the same for the two wires and simplify in the ratio, and we get:
By using the resistivity of the aluminum:
and the resistivity of the tungsten: 
m we can get the resistance of the tungsten wire:
where
Using this formula, and labeling with A the aluminum and with T the tungsten wire, we can write the ratio between
the two wires are identical, so L and A are the same for the two wires and simplify in the ratio, and we get:
By using the resistivity of the aluminum: