Question
What is electrical resistivity of a material? State its SI unit and define it.

Answer

It is found that the resistance $R$ of a uniform metallic conductor depends on its length 1. on its area of cross-section $A$, the nature of its material and temperature.
$\rightarrow$ Precise measurements have shown that at a given temperature,
$R \propto l$ and $R \propto \frac{1}{A}$
Combining above two relations,
$
\begin{array}{l}
R \propto \frac{l}{A} \\
\therefore R=\rho \frac{l}{A}
......(11.6)\end{array}
$
Where $\rho$ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor.
$\rightarrow$ From equation (11.6),
$
\rho=\frac{R A}{l}
......(11.7)$
$\therefore$ The SI unit of $\rho$
The SI unit of resistance $\times$
$
\begin{array}{l}
=\frac{\text { The SI unit of area of cross-section }}{\text { The SI unit of length }} \\
=\frac{\Omega m^2}{m} \\
=\Omega m \text { (ohm-metre) }
\end{array}
$
$\rightarrow$ In equation (11.7), if $A=1$ unit and $l=1$ unit. $\rho=R$.
The electrical resistivity of a material is the resistance of a conductor (of that material) having unit length and unit area of cross-section.
[Notes: (1) Resistivity depends on temperature.
(2) Resistivity is also called specific resistance.]

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