Two copper wires A and B are of the same thickness and are at the room temperature. If the length of A is twice the length of B then :

(a) Compare their resistances

(b) Compare their resistivity

(a) Let the length of wire B be L and that of A be 2L

R= ρ$\dfrac{\text{length}}{\text{area}}$

As area and specific resistance (ρ) are same for both wires A and B,

Hence,

$\dfrac{\text{R}$a}{\text{R}b} = $\dfrac{\text{l}$a}{\text{l}b} = $\dfrac{\text{2L}}{\text{L}}$ = $\dfrac{\text{2}}{\text{1}}$

Hence, the ratio between resistances A and B is 2 : 1

(b) Both the wires will have the same specific resistance because the specific resistance is a characteristic property of the material and as both the wires are of copper hence both will have same specific resistance.