The resistivity $\rho$ of a material may be expressed in units of

The resistivity $\rho$ of a material may be expressed in units of

ohm
ohm/cm
ohm-cm
ohm-cm$^2$
This question was previously asked in
UPSC CDS-1 – 2020
Resistivity ($\rho$) is a fundamental property of a material that quantifies how strongly it resists the flow of electric current. Resistance ($R$) of a conductor is related to its resistivity, length ($L$), and cross-sectional area ($A$) by the formula $R = \rho \frac{L}{A}$. Rearranging this formula to solve for $\rho$, we get $\rho = R \frac{A}{L}$.
The unit of resistance ($R$) is Ohm ($\Omega$). The unit of area ($A$) is typically square meters (m²) or square centimeters (cm²). The unit of length ($L$) is typically meters (m) or centimeters (cm). Substituting these units into the formula for $\rho$: $\text{Units of } \rho = \Omega \times \frac{\text{cm}^2}{\text{cm}} = \Omega \cdot \text{cm}$. Alternatively, using meters: $\text{Units of } \rho = \Omega \times \frac{\text{m}^2}{\text{m}} = \Omega \cdot \text{m}$. Therefore, the resistivity is commonly expressed in ohm-centimeters ($\Omega \cdot \text{cm}$) or ohm-meters ($\Omega \cdot \text{m}$).
While both ohm-meter ($\Omega \cdot \text{m}$) and ohm-centimeter ($\Omega \cdot \text{cm}$) are valid units for resistivity, ohm-centimeter is also widely used, particularly in semiconductor physics and some older standards. Option C correctly identifies ohm-cm as a unit for resistivity.