What is the SI unit of resistivity?
- $\Omega \mathrm{m}$
- $\Omega \mathrm{m}^{-1}$
- $\Omega^{-1} \mathrm{~m}^{-1}$
- $\Omega \mathrm{m}^{-2}$
Solution
The resistance $R$ of a conductor follows the relationship $R = \rho \frac{L}{A}$, where $\rho$ represents resistivity, $L$ is length, and $A$ is cross-sectional area.
Solving for resistivity yields $\rho = R \frac{A}{L}$.
Substituting SI units: $\Omega$ for resistance, m$^2$ for area, and m for length, we obtain $\Omega \cdot \frac{\mathrm{m}^2}{\mathrm{m}} = \Omega \cdot \mathrm{m}$.
The SI unit of resistivity is ohm-meter ($\Omega \cdot \mathrm{m}$).
Among the options, only choice A correctly represents this unit.
Asked in: MHT CET 2025 (05 May Shift 2)