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 $l$, on its area of crosssection $A$, the nature of its material and temperature.
- Precise measurements have shown that at a given temperature,
- $R \propto l$ and $R \propto \frac{1}{A}$
- Combining above two relations,
- $R \propto \frac{l}{A}$
- $\therefore R =\rho \frac{l}{A} \ldots . . .(12.6)$
- Where $\rho$ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor.
- From equation $(12.6),$
- $\rho=\frac{R A}{l}.......(12.7)$
- $\therefore$ The $SI$ unit of $\rho$
- The SI unit of resistance $x$
- $=\frac{\text { The SI unit of area of cross-sections }}{\text { The SI unit of length }}$
- $=\frac{\Omega m ^2}{m}$
- $=\Omega m \text { (ohm-metre) }$
- In equation $(12.7)$, 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.
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