Question

Which of the following will be constant across the length of a conductor of non-uniform cross section, when a steady current flows through it?
1. Current and drift velocity
2. Drift velocity only
3. Current only
4. None of the above

Answer 1

Correct Answer - Option 3 : Current only

The correct answer is option 3) i.e. Current only

CONCEPT:

• Drift velocity: The average velocity attained by the electrons under the influence of an electric field is termed the drift velocity. 
  • The free electrons are always in a constant random motion in the conductor.
  • When the conductor is connected to a battery, an electric field is generated.
  • When these free electrons are subjected to an electric field, they slowly drift in the direction of the electric field applied, while maintaining the random motion.
  • At this point, the net velocity of the electrons is called its drift velocity.

The drift velocity (vd) of the electron in a conductor is given by:

\(v_d =\frac{I}{nAq}\)

Where I is the current flowing through the conductor, A is the area of cross-section of the conductor, q is the charge on the electron and n is the number of electrons.

EXPLANATION:

• Drift velocity, \(v_d \propto \frac{1}{A}\). Since the cross-sectional area is non-uniform, v_d varies throughout the length of the conductor.
• Hence, only the current through the conductor would remain constant.