If the temperature of a metallic conductor rises, with the same potential difference across it, what happens to the drift velocity of the electrons?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → It decreases.
The free electrons in a metal drift with speed \( v_d=eE\tau/m \), where \( \tau \) is the relaxation time, the average time between collisions. The same potential difference across the same conductor keeps the field \( E=V/l \) unchanged. So \( v_d \) changes only through \( \tau \).
Option (1) It increases. — Incorrect. A higher temperature makes the electrons collide more often, so \( \tau \) becomes shorter. A shorter \( \tau \) gives a smaller drift speed.
Option (2) It decreases. — Correct. As the temperature rises, the electrons move faster on average and collide more often. So \( \tau \) decreases with temperature. With \( E \) unchanged, \( v_d=eE\tau/m \) decreases.
Option (3) It remains the same. — Incorrect. The field stays the same, but the drift speed also depends on \( \tau \), which changes with temperature.
Option (4) It cannot be said. — Incorrect. The given conditions fix both factors. The same potential difference keeps \( E \) the same, and \( \tau \) falls with temperature. So the change is definite.
NCERT (2026-27):
Drift of Electrons and the Origin of Resistivity – “… The average value of ti then is τ (known as relaxation time). Thus, averaging … over the N-electrons at any given time t gives us for the average velocity vd”
\( \displaystyle v_d=(v_i)_{\mathrm{average}}=-\frac{eE}{m}\,(t_i)_{\mathrm{average}}=-\frac{eE}{m}\,\tau \)\( \qquad (3.17) \)
Temperature Dependence of Resistivity – “… As we increase temperature, average speed of the electrons, which act as the carriers of current, increases resulting in more frequent collisions. The average time of collisions τ, thus decreases with temperature.”