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Mathematically, by relating the intrinsic quantities like drift velocity,relaxation time etc., it is easy to show that

$$\rho=\frac{E}{J}$$

and

$$R=\frac{V}{i}$$

are true.

But, is it correct to say the the first equation is really a generalisation of the second equation? If yes why?

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$\rho$ is a property of a material, $R$ is a property of a resistor or some other specific object made out of some material or a combination of materials. They are related, but neither one is a generalization of the other.

A close analogy is density and mass. They are related, but you cannot say that a mass is a special kind of a density or density is special kind of a mass.

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