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