Two wires have the same length, but the second has twice the diameter of the first. Find the resistance of the second wire if the resistance of the first is 4Ω .

Answer 1

Resistance of a wire is proportional to the length and inversely proportional to the cross-sectional area.

If the diameter of the first wire is D, its area is pi x D² / 4 and the area of the second wire is pi x (2D)² / 4 or pi x D². The area of the second wire is 4 times the area of the first wire and has 1/4 the resistance of the first wire.

As the first wires resistance is 4 ohms, the resistance of the second wire is 1 ohm.