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
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(a) Let the length of wire B be L and that of A be 2L
R= ρ$\frac{\text{length}}{\text{area}}$
As area and specific resistance (ρ) are same for both wires A and B,
Hence,
$\frac{\text{R}_a}{\text{R}_b}$ = $\frac{\text{l}_a}{\text{l}_b}$ = $\frac{\text{2L}}{\text{L}}$ = $\frac{\text{2}}{\text{1}}$
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.