A cylindrical metal rod is 2.40 m long and 5.99 mm in diameter. The resistance between its two ends (at 20oC) is 1.38 * 10-3 Ω. (a) What is the material? (b) A round disk, 2.24 cm in diameter and 1.20 mm thick, is formed of the same material. What is the resistance between the round faces, assuming that each face is an equipotential surface?

(a) silver

(b) 4.94 x 10^-8 ohm

Explanation:

L = 2.4 m

diameter = 5.99 mm = 5.99 x 10^-3 m

Radius, r = diameter / 2 = 2.995 x 10^-3 m

R = 1.38 x 10^-3 ohm

(a) Let ρ be the resistivity of the material

R = ρ L / A

R A / L = ρ

ρ = (1.38 x 10^-3 x 3.14 x 2.995 x 10^-3 x 2.995 x 10^-3) / 2.4

ρ = 1.62 x 10^-8 ohm-m

The material is silver.

(b) t = 1.2 mm = 1.2 x 10^-3 m

Diameter = 2.24 cm = 0.0224 m

Radius, r = 0.0112 m

Resistance, R = ρ x t / A

R = 1.62 x 10^-8 x 1.2 x 10^-3 / (3.14 x 0.0112 x 0.0112)

R = 4.94 x 10^-8 ohm