Question
What is resistivity ? On What factors does it depend and write its unit and dimensional formula.

Answer

Resistance of material
$R =\frac{ ρ l}{A}$
where $ρ =$ resistivity of conductor
$\therefore ρ=\frac{R A}{l}$
If we take $A =1$ unit $\left( A =1 m^2\right)$ and $l=1$ unit $(l=1 m)$ then $\rho= R$.
Definition : Resistance of a conductor having unit cross- sectional area and unit length is called resistivity.
The magnitude of resistivity depends on the type of material and temperature but it does not depend on the dimensions of material.
The unit of resistivity is $\Omega m$ and its dimensional formula $M ^1 L^3 T^{-3} A^{-2}$.

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