Question

The resistance of a metal wire of length 1 m is 26 Ω at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature?

Answer 1

Given: Current (I) = 1 m

Resistance (R) = 26 Ω

Diameter (d) = 0.3 mm

Radius (r) = `d/2`

r = `0.3/2`

r = 0.15 mm

r = 0.15 × 10⁻³m

Cross-sectional area (A) = `(pi d^2)/4`

A = `(3.14 xx (3 xx 10^-8)^2)/4`

A ≈ 7.0686 × 10⁻⁸ m²

We know that,

Resistivity (ρ) = `R xx A/l`

ρ = `(26 xx 7.0686 xx 10^-8)/1`

ρ = 1.84 × 10⁻⁶ Ω m