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) R = ρ $\dfrac{l}{a}$ = ρ $\dfrac{l}{πr^2}$

Resistance for wire of radius 1 mm,

R₁ = ρ $\dfrac{l}{π1^2}$ = ρ $\dfrac{l}{π}$

Resistance for wire of radius 2 mm,

R₂ = ρ $\dfrac{l}{π2^2}$ = ρ $\dfrac{l}{π4}$

Hence, ratio between the two,

R₁ : R₂

$= \dfrac{ρ\dfrac{l}{π}}{ρ\dfrac{l}{π4}} \\[1em] = \dfrac{4}{1} \\[0.5em] = 4 : 1$

Hence, the ratio of resistance between the two wires = 4 : 1

(ii) The specific resistance of the two wires will be same because the specific resistance is a characteristic property of the material, hence it does not change with radius.

Therefore, ratio of specific resistance between the two wires = 1 : 1