Question

A current passes through a wire of non-uniform crosssection. Which of the following quantities are independent of the cross-section?

• A. The charge crossing in a given time interval
• B. Drift speed
• C. Current density
• D. Free-electron density

Answer 1

Answer: (A), (D)

The correct options are
A The charge crossing in a given time interval
D Free-electron density

By conservation of charge and continuity equation, the current is same throughout a wire. Because current is defined as the charge crossing in a given time interval, option A is correct.

By definition, $I=nq{v}_d$ , where, $v_d$, is the drift velocity. It varies with cross section. So, B is incorrect. Due to non uniformity of cross section, the current density, defined as

Current density $=\frac{Current}{Area}$ varies. So C is incorrect.

The charge carrier density or free electron density is a property of material and temperature only. It does not depend upon cross section. So, D is correct.