Drift velocity of free electrons in a metallic conductor is independent of
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Average thermal velocity of free electrons
Note: The given answer is as per the official NTA Answer Key. However, the question can have more than one correct answer, i.e. both Option (3) and Option (4), as explained below.
An applied field gives each free electron an acceleration \( eE/m \) between collisions; averaged over all electrons, the random thermal velocities cancel and only the drift velocity remains:
\( \displaystyle v_d = \frac{eE\tau}{m} \)
where \( \tau \) is the relaxation time.
Option (1) Temperature of conductor — Incorrect. A higher temperature makes collisions more frequent, so \( \tau \) and \( v_d \) decrease.
Option (2) Applied Electric field — Incorrect. \( v_d \) is directly proportional to E.
Option (3) Length of conductor — Correct. \( v_d = eE\tau/m \) contains no length, so for a given field it does not depend on length.
Option (4) Average thermal velocity of free electrons — Correct. The thermal velocities are random in direction, so their average is zero and adds nothing to the drift.