Drift velocity of electrons is directly proportional to the :

The correct answer is Option (2) → Voltage applied

The drift velocity is the average velocity the electric field gives the electrons between collisions:

    \( \displaystyle v_d = \frac{e E \tau}{m} \)

For a conductor of length \( l \) with a potential difference \( V \) across it, \( E = V/l \), so

    \( \displaystyle v_d = \frac{e \tau}{m l}\,V \;\Rightarrow\; v_d \propto V \)

The drift velocity is directly proportional to the applied voltage.

Option (1) Temperature — Incorrect. A rise in temperature shortens the relaxation time \( \tau \), so \( v_d \) decreases, not increases.

Option (2) Voltage applied — Correct. \( v_d = e\tau V/(m l) \), so \( v_d \propto V \).

Option (3) Length of the conductor — Incorrect. For a given voltage, \( v_d \propto 1/l \); it is inversely proportional to the length.

Option (4) Area of cross section of conductor — Incorrect. For a given voltage, \( v_d \) does not depend on the area of cross-section.

NCERT (2026-27):
Drift of Electrons and the Origin of Resistivity – “… Thus, averaging Eq. (3.16) over the N-electrons at any given time t gives us for the average velocity v_d

    \( \displaystyle \mathbf{v}_d = -\frac{e\mathbf{E}}{m}\,\tau \qquad (3.17) \)

… This is the phenomenon of drift and the velocity v_d in Eq. (3.17) is called the drift velocity.”