The formula for resistivity is: $$\rho = \frac{RA}{L}$$ where $\rho$ is resistivity, $R$ is resistance, $A$ is cross-sectional area, and $L$ is the length of the conductor.
We can see from the formula that $A$ and $L$ are involved, why then does resistivity not depend on dimensions?
Best Answer
It's because resistance ($R$) is also a function of size.
A short and wide section of a material will have lower resistance than a long thin section of the same material. Larger cross sections have less resistance, and longer conductors have more resistance.
Therefore, by multiplying resistance by area and dividing by length, you get a value for a material property (resistivity $\rho$) that doesn't depend on the size of the conductor.
That is the point of resistivity, to be applicable to a material over various cross sections and lengths.