A current passes through a wire of non-uniform cross-section. Which of the following quantities are independent of cross-section?
A. Drift speed
B. Current density
C. Free electron density
D. The charge crossing in a given time interval.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → C and D only
In steady flow, charge cannot pile up anywhere in the wire, so the current is the same at every cross-section. The current is linked to the other quantities by
\( \displaystyle I = neAv_d \)
With I and n fixed, a smaller area A needs a larger drift speed, and the current density \( j = I/A \) is larger there.
(A) Drift speed — Incorrect. \( v_d = I/(neA) \) is larger where the wire is thinner.
(B) Current density — Incorrect. \( j = I/A \) also changes with A.
(C) Free electron density — Correct. n is the number of free electrons per unit volume, a property of the material, and the material is the same throughout.
(D) The charge crossing in a given time interval. — Correct. This is the current multiplied by the time, and the current is the same at every cross-section.
Note: A similar question was also asked in CUET (UG) 2026 on 21-05-2026 (Slot 1).