The resistivity of a material depends on

The correct answer is Option (3) → nature and temperature of material

The resistivity \( \rho \) is a property of the material, defined through \( R = \rho l/A \). The resistance \( R \) depends on the dimensions \( l \) and \( A \), but \( \rho \) does not: it depends on the nature of the material and on its temperature.

Option (1) length, area of cross section and temperature of material — Incorrect. Length and area belong to the resistance, not to the resistivity.

Option (2) length and area of cross section of material — Incorrect. Same reason; and the dependence on the material is left out.

Option (3) nature and temperature of material — Correct. The resistivity of copper differs from that of nichrome (nature), and it changes with temperature.

Option (4) temperature of material only — Incorrect. Temperature matters, but the material itself matters too.

NCERT (2026-27):
Ohm’s Law – “… Combining Eqs. (3.5) and (3.7), we have

    \( \displaystyle R \propto \frac{l}{A} \qquad (3.8) \)

and hence for a given conductor

    \( \displaystyle R = \rho\,\frac{l}{A} \qquad (3.9) \)

where the constant of proportionality ρ depends on the material of the conductor but not on its dimensions. ρ is called resistivity.”

Temperature Dependence of Resistivity – “The resistivity of a material is found to be dependent on the temperature.”