Skin effect is proportional to

Question

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Option C: Directly proportional to (Diameter of conductor)2

Explanation & Concepts:
The skin effect is the tendency of an alternating electric current to distribute itself within a conductor such that the current density is highest near the surface and decreases exponentially towards the center. The depth of this penetration, known as the skin depth ($\delta$), is inversely proportional to the square root of frequency, while the effective resistance of the conductor increases with the square of the conductor diameter at high frequencies.

Working Principle: As AC flows through a conductor, the varying magnetic field within the conductor induces eddy currents that oppose the main current flow at the center, forcing current towards the surface. The effective cross-sectional area used for conduction is reduced, thereby increasing the AC resistance. The phenomenon is significant at high frequencies or for conductors with large diameters.

Key Formulas: $R_{ac} \approx R_{dc} 	imes (1 + k \cdot d^2)$ — Relationship showing AC resistance increase with conductor diameter $d$ at higher frequencies; $\delta = \sqrt{\frac{1}{\pi f \mu \sigma}}$ — Skin depth equation showing inverse relationship with square root of frequency

Key Points: Skin effect increases the effective AC resistance of a conductor.; It is more pronounced in conductors with larger cross-sectional areas (larger diameters).; It is directly dependent on the frequency of the alternating current.; For power frequency (50 Hz), the skin effect is minimal in copper/aluminum conductors of standard transmission line sizes.

Advantages: Used in induction heating processes.; Reduces interference in shielded cables.

Disadvantages: Increases power loss in transmission lines due to higher AC resistance.; Requires inefficient use of conductor material at high frequencies.

Applications: High-frequency transmission lines; Induction hardening of steel; Surface treatment of metals

Additional Info: At very high frequencies, the current flows only in a very thin surface layer, making the internal material of the conductor redundant.. Option A and B represent square root dependencies which apply to skin depth, not resistance behavior. The question specifically refers to the magnitude of the effect on resistance/impedance, leading to the $d^2$ relationship.

Answer: C is correct — The AC resistance of a conductor due to skin effect increases in proportion to the square of the conductor diameter ($d^2$).

Exam Tip: Always distinguish between skin depth (which decreases with diameter) and skin effect resistance (which increases with diameter/frequency).

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Option A: Directly proportional to (Diameter of conductor)1/2

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Option B: Inversely proportional to (Diameter of conductor)1/2

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Option D: Inversely proportional to (Diameter of conductor)2

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