Two wires of the same material and same length have radii 1 mm and 2 mm respectively. Compare (i) their resistances (ii) their specific resistance.

(i) When the radius of wire is r₁ 

R₁ = ρ (l / A₁)

R₁ = ρ (l / πr₁²)

(ii) When the radius of wire is r₂

R₂ = ρ (l / A₂)

R₂ = ρ (l / πr₂²)

∴ R₁: R₂ will be

ρ (l / πr₁²) : ρ (l / πr₂²)

= r₂²: r₁²

(ii) Because the two wires are made of the same material, their resistivity will be the same. That is

ρ₁: ρ₂ = 1: 1