Question

Given below are two statements:
Statement (I): Direct current flowing the conductor gets uniformly distributed
Statement (II): An alternating current flowing through the conductor does not distribute uniformly.
In light of the above statements, choose the most appropriate answer from the options given below.

• A. Both Statement (I) and Statement (II) are true.
• B. Both Statement (I) and Statement (II) are false.
• C. Statement (I) is true but Statement (II) is false.
• D. Statement (I) is false but Statement (II) is true.

Hint:

At high frequencies, the skin effect is so pronounced that current flows almost entirely along a thin outer layer of the conductor. This is why hollow conductors or stranded Litz wire are often used in high-frequency applications.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The spatial distribution of electrical current across a conductor's cross-section is determined by whether the current is steady (DC) or time-varying (AC). This is due to the presence of electromagnetic induction in AC systems.
Key Formula or Approach:
The skin depth (\(\delta\)) characterizes how deeply an electromagnetic wave or current can penetrate a conductor, and is defined as: \[ \delta = \sqrt{\frac{\rho}{\pi f \mu}} \] where \(\rho\) is resistivity, \(f\) is frequency, and \(\mu\) is magnetic permeability.

Step 2: Detailed Explanation:
Let us analyze the two statements:

Statement (I): For Direct Current (DC), the frequency is zero (\(f = 0\)).
Substituting \(f = 0\) into the skin depth relation yields an infinite skin depth (\(\delta \rightarrow \infty\)).
Since DC is steady over time, it does not produce a changing magnetic flux, meaning no back-EMF is induced within the conductor.
Consequently, the current density is completely uniform across the entire cross-section of the conductor. Thus, Statement (I) istrue.

Statement (II): For Alternating Current (AC), the frequency is non-zero (\(f > 0\)).
The time-varying current produces a changing magnetic field that induces opposing eddy currents within the conductor's interior.
This causes the current density to decrease exponentially from the outer surface toward the center.
As a result, current distribution becomes non-uniform, concentrating near the surface. Thus, Statement (II) istrue.
Since both Statement (I) and Statement (II) are true, Option (A) is the correct choice.

Step 3: Final Answer:
Both Statement (I) and Statement (II) are true, which corresponds to Option (A).