Question

How does the resistance of a wire vary with its:

(a) area of cross-section?
(b) diameter?

Answer 1

(a)The resistance of a conductor is inversely proportional to its area of cross-section, i.e. R α 1 / A. So on increasing the area of cross-section, its resistance will decrease.

(b) We know that the area of cross-section, A = πr² = π (d / 2)², where r is the radius and d is the diameter of the wire. So on increasing the diameter of the wire, its resistance decreases.