What is resistivity ? On What factors does it depend and write it… - Vidyadip

Question

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

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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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