The resistance of a wire of length 31.4 m and diameter 1 mm is 20 Ω . Find the resistivity of the material of the wire.

Solution: Data : l = 31.4 m, d = 1mm = 1× 10 ^{- 3} m

∴ r = d/2 = (1× 10^-3m)/2 = 5× 10^-4 m , R = 20 Ω , ρ = ?

R = ρ (l/A) = ρ (l/π r²)

∴ ρ = (Rπr²)/l

∴ ρ = 20Ω × 3.14 × (5× 10^-4 m)² / 31.4m

∴ ρ = 5× 10^-7Ω .m

The resistivity of the material of the wire = 5 × 10^-7 Ω m.