Question

A 6 m long wire has diameter 0.5 mm. Its resistance is 50 Ω. Find the resistivity and conductivity.

Answer 1

Given: l = 6 m,

D = 0.5 mm,

r = 0.25 mm = 0.25 × 10⁻³ m,

R = 50 Ω

To find: i. Resistivity (ρ)

ii. Conductivity (σ)

∴ ρ = `(R A)/l`

`rho = (R pi r^2)/l`

ρ = `(50 xx 3.142 xx (0.25 xx 10^-3)^2)/6`

ρ = 1.636 × 10⁻⁶ Ω m

∴ σ = `1/rho`

∴ σ = `1/(1.636 xx 10^-6)`

= 0.612 × 10⁻¹ × 10⁶     ....(Using reciprocal from log table)

= 6.12 × 10⁵ Ω⁻¹ m⁻¹