Question

The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 50 feet long and 3 millimeters in diameter has a resistance of 0.255 ohm, find the length of a wire of the same material whose resistance is 0.147 ohm and whose diameter is 2.5 millimeters.

Answer 1

Given The Resistance 'R' of a wire varies directly with the length of the wire 'l' and inversely with the square of diameter 'd'

That is

or , where k is a constant

Its given, R = 0.225ohm when the wire is 50 feet and 3millimeters

or

or

Substituting this with the new values, we get

Note : We are not converting feet and milimeters into an equation unit of measurement, because we will use the same type of measurement in their respective places in both the cases, and it will cancel each other out