The electrical resistance of a wire varies directly with the length and inversely with the square of the diameter of the wire

Question

If a wire 432 feet long and 4 millimeters in diameter has a resistance of 1.24 ohms, find the length of a wire of the same material whose resistance is 1.44 ohms and whose diameter is 3 millimeters.

Answer 1

if the relationship is linear, then

Let R = Resistance

L = Length

D = Diameter

k = Proportionality Constant

then

R = k(L/D). We must find k: k = (DR)/L = (4*1.24)/432 = .01148

Then to find the length of new wire,

1.44 = (.01148)(L/3) or. L = 376 feet

It is strange that you mix metric & English units but the proportional constant will compensate!