The electrical resistance $R$ and electrical resistivity $\rho$ of a metal wire are related by $$\rho=\frac{RA}{l}$$ where $l$ is the length and $A$ is the cross-sectional area of the wire. One could also have written $$R=\frac{\rho l}{A}.$$ From the first relation, it implies that resistivity is a geometric property of the conductor while the second relation implies that resistance is a geometric property. However, I know that resistance is a geometric property while resistivity is an intrinsic property. See here. But it's not clear to me why.
[Physics] Resistance and resistivity: which one is the intrinsic and which is the geometric property? Why
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Best Answer
Resistivity is the resistance of a given material when the material is of unit length and unit area. So, resistivity is an intrinsic property. Resistance changes with the material geometry, for example, the resistance of the material is doubled when length of the material is doubled and halved when area of cross-section of the material is doubled. However, in both the above cases, the resistivity of the material remains the same because it is still calculated over a unit length and a unit area of the material.