Consider two copper wires. One has twice the length of the other. How do the resistivities of these two wires compare?
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The resistivity of a material using which a resistor is made is constant. It does not depend on the dimensions of the resistor though it may vary with other factors like temperature.
If two copper wires are being considered, one of which is two times as long as the other, the resistivity of both is the same. The resistance of each of the wires is given by `R = rho*l/A` where `rho` is the resistivity, l is the length and A is the cross-sectional area.
The resistance of the wire with twice the length will be twice that of the other wire. But this not influence the resistivity of the wires; this is the same in both the cases.
Resistivity of a conductor depends on the material of the conductor and its temperature, not on the shape,length or area of cross section.
R= pl/a
now p=Ra/l
For the second wire, length=2l
R is directly proportional to l.
So, p=2Ra/2l=Ra/l.
Hence, resistivity is same for both since both the wires are made of copper.
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