The resistivity of a wire depends on :(A) its length(B) its area of c…

The correct answer is Option (3) → (C) and (D) only

Resistivity is a property of the material, not of the shape of a particular wire. For a conductor

    \( \displaystyle \rho = \frac{m}{n e^{2} \tau} \)

where \( n \) is the number of free electrons per unit volume (fixed by the material) and \( \tau \) is the relaxation time (which falls as the temperature rises).

(A) its length — Incorrect. Length changes the resistance \( R = \rho l/A \), but \( \rho \) itself does not depend on the dimensions.

(B) its area of cross-section — Incorrect. For the same reason, area affects the resistance, not the resistivity.

(C) its temperature — Correct. A higher temperature makes the ions vibrate more, so collisions are more frequent, \( \tau \) falls and \( \rho \) rises.

(D) nature of material — Correct. Each material has its own \( n \) and \( \tau \), which is why copper and nichrome have very different resistivities.

(E) voltage applied across it — Incorrect. For an ohmic wire the current is proportional to the voltage, so \( V/I \), and with it \( \rho \), does not change with the applied voltage.

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 average time of collisions τ, thus decreases with temperature. In a metal, n is not dependent on temperature to any appreciable extent and thus the decrease in the value of τ with rise in temperature causes ρ to increase as we have observed.”