Question

If the supply frequency increases, the Skin Effect in a conductor:

• A. Increases
• B. Decreases
• C. Remains the same
• D. Becomes zero

Hint:

To mitigate the skin effect at high frequencies, conductors are made hollow, or multiple stranded conductors (such as ACSR or Litz wire) are used instead of a single solid conductor.
Skin effect is completely absent in pure DC circuits because the frequency is zero (\(f = 0\)).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks about the relation between the frequency of the AC supply and the skin effect in an electrical conductor.

Step 2: Key Formula or Approach:
The skin effect refers to the tendency of an alternating electric current to distribute itself within a conductor so that the current density is larger near the surface of the conductor.
This behavior is quantified by the skin depth (\(\delta_s\)), which is defined as:
\[ \delta_s = \sqrt{\frac{\rho}{\pi f \mu}} \] where:
- \(\rho\) is the resistivity of the conductor.
- \(f\) is the frequency of the alternating current.
- \(\mu\) is the magnetic permeability of the conductor.

Step 3: Detailed Explanation:

• From the skin depth formula, we see that skin depth is inversely proportional to the square root of the frequency:
\[ \delta_s \propto \frac{1}{\sqrt{f}} \]
• As the supply frequency \(f\) increases, the skin depth \(\delta_s\) decreases.

• A smaller skin depth means that the current is confined to a thinner layer near the outer surface of the conductor.

• Consequently, the effective cross-sectional area through which the current flows is reduced.

• Since resistance is inversely proportional to cross-sectional area (\(R = \frac{\rho L}{A}\)), the effective AC resistance of the conductor increases.

• Thus, an increase in supply frequency causes the skin effect to increase.

Step 4: Final Answer:
If the supply frequency increases, the skin effect increases.