Question

Across a metallic conductor of non-uniform cross section a constant potential difference is applied. The quantity which remains constant along the conductor is:

• A. drift velocity
• B. electric field
• C. current density
• D. current

Hint:

The potential difference across the metallic conductor is non-uniform in nature. The cross-section of the metallic conductor is also non-uniform. 

Answer 1

The Correct Option is D

To solve this problem, we need to consider the properties of electric current in a conductor with non-uniform cross-section under a constant potential difference. Let's analyze the options:

1. Drift velocity: The drift velocity of charge carriers in a conductor is given by the formula: v_d = \frac{I}{nqA}, where \( I \) is the current, \( n \) is the number density of electrons, \( q \) is the charge of an electron, and \( A \) is the cross-sectional area. In a conductor of non-uniform cross-section, \( A \) varies along its length. Hence, drift velocity will not remain constant.
2. Electric field: The electric field \( E \) in a conductor is related to the potential difference and distance along the conductor. It is expressed by: E = \frac{V}{L}, where \( V \) is the potential difference and \( L \) is the length of the conductor. However, the field may vary due to changes in resistivity or cross-sectional area along the conductor, so it is not necessarily constant.
3. Current density: Current density \( J \) is defined as: J = \frac{I}{A}. Since the area \( A \) can vary in a non-uniform conductor, the current density will also change accordingly.
4. Current: The current \( I \) is defined as the rate of flow of charge. According to the principle of conservation of charge, in a closed circuit, the same amount of charge that enters a junction must leave. Hence, current remains constant throughout the conductor, regardless of changes in cross-section.

Based on the above analysis, the quantity that remains constant along the conductor is the current.

Therefore, the correct answer is: current.