A current passes through a conducting wire of non-uniform cross-section. Which of the following quantities will remain the same throughout the wire?
(A) The charge passing in a given time interval
(B) Drift speed
(C) Current density
(D) Free-electron density
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (D) only
In a steady current the same charge must pass every cross-section each second (conservation of charge), so I is the same everywhere along the wire, while the area A changes.
\( I = neAv_{d} \)
\( j = I/A \)
(A) The charge passing in a given time interval — Correct. This is the current, which is the same at every cross-section.
(B) Drift speed — Incorrect. \( v_{d} = I/(neA) \) is larger where the wire is thinner.
(C) Current density — Incorrect. \( j = I/A \) also varies inversely with the area.
(D) Free-electron density — Correct. n is a property of the material, and the wire is of one material throughout.
Note: A similar question was also asked in CUET (UG) 2026 on 31-05-2026 (Slot 2).