Identify the incorrect statement(s) from the following in the context…

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

(A) The electrons suffer collisions with heavy fixed ions in the conductor — Correct. The free electrons drift through a lattice of positive ions and keep colliding with the ions; these collisions are the origin of resistance.

(B) The resistance of the given conductor depends on its temperature — Correct. Heating makes the ions vibrate more and shortens the relaxation time, so the resistance of a metal rises with temperature.

(C) Resistance and resistivity both depend on the dimensions of the conductor — Incorrect. Resistance depends on the dimensions, \( R = \rho l/A \), but resistivity is a property of the material (at a given temperature) and does not depend on the length or the area.

(D) When a potential difference V is applied across the conductor then V = IR — Correct. This is Ohm's law: the current is proportional to the applied potential difference, with \( R \) the resistance.

NCERT (2026-27):
Ohm’s Law – “… Then Ohm’s law states that

    \( \displaystyle V \propto I \quad \text{or,} \quad V = R\,I \qquad (3.3) \)

where the constant of proportionality R is called the resistance of the conductor. … The resistance R not only depends on the material of the conductor but also on the dimensions of the conductor.”

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 \( \rho \) depends on the material of the conductor but not on its dimensions. \( \rho \) is called resistivity.”