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

The correct option is(D): current.

As all the cross sections of the conductor are considered to be in series, the current should be constant.

We will identify the quantity unaffected by the non-uniformity of the metallic conductor. 

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

Current is the amount of charge passing through a point in a given time. The rate of flow of charge is also termed as current. It is measured in amperes. It does not depend on any physical characteristics of the medium. If a medium is conducting in nature, then a charge will flow through it.

Drift velocity is the average velocity acquired by charged particles like electrons, in a material as a result of an electric field. Applying an electric field applies a net flow in a direction, known as the drift.

Electric field is electric force per unit charge. It depends upon the separation of the test charge and the electric field and the charge produced by the electric field.

Current density refers to the amount of charge passing through a unit area in a unit of time. However, if the material is non-uniform, then the current density will also be non-uniform. 

Hence, from the above explanation, it is clear that current is not affected when a constant potential difference is applied across a non-uniform metallic conductor.

Thus, the correct option is D) current.

Note: Current just depends on the potential difference applied across a conductor. However, the flow of current is affected by the resistance in it. The higher the resistance, the lesser the current flow, or vice-versa.

Answer 2

The correct option is D: Current

Explanation:

Current is the charge flown per unit of time. It should remain the same along any cross section as no accumulation of charge is there in the conductor. Therefore, current remains constant.

• The resistance is given by R = ρL/A, where ρ is resistivity (constant for a given material). When the area of the cross-section of the resistor varies, the resistance also varies.
• According to Ohm's law, V=IR. As I is constant and R varies, the potential difference varies along the cross-section and hence the electric field also changes in the cross-section.
• Drift velocity can be found by v_d​=I​/neA which also changes as I stay constant and A varies.
• Current density is given as J=I/A​. As A varies and I stay constant, the current density also changes.

Hence, the correct answer is option D) Across a metallic conductor of non-uniform cross-section a constant potential difference is applied. The quantity which remains constant along the conductor is current