Skin effect in conductor is proportional to

Question

Examoogle · Accepted Answer

Option C: Square of conductor diameter

Explanation & Concepts:
The skin effect is the tendency of an alternating electric current to become distributed within a conductor such that the current density is highest near the surface and decreases exponentially towards the center. The skin effect ratio, which relates the AC resistance to DC resistance, is directly proportional to the square of the conductor diameter (or more precisely, proportional to $d^2f$).

Working Principle: As AC flows through a conductor, the internal magnetic flux linkages are higher at the center than at the surface due to the geometry of the conductor. This leads to higher self-inductance at the center, creating a greater inductive reactance that opposes the flow of current. Consequently, electrons are forced towards the outer periphery, reducing the effective cross-sectional area and increasing the effective resistance.

Key Formulas: $R_{ac} = R_{dc} [1 + \frac{1}{3}(\frac{m^2 d^2}{4})^2]$; $\delta = \frac{1}{\sqrt{\pi f \mu \sigma}}$ — Skin depth equation

Key Points: Skin effect increases with an increase in frequency, conductor diameter, permeability, and conductivity.; At DC (f = 0), current is distributed uniformly across the entire cross-section of the conductor.; The skin effect is negligible for small diameter conductors and low frequencies (e.g., 50 Hz).; AC resistance is always greater than DC resistance due to non-uniform current distribution.

Advantages: Used in induction heating processes.; Useful in surface hardening of steel components.

Disadvantages: Increases transmission line power losses ($I^2R$).; Increases the effective resistance of the conductor, leading to voltage drop.; Reduces the ampacity (current-carrying capacity) of the conductor.

Applications: High-voltage AC transmission lines.; Radio frequency (RF) circuits.; Induction heating systems.

Additional Info: The depth of penetration (skin depth) $\delta$ is the distance from the surface where current density drops to $1/e$ or approximately 37% of the surface value.. Option A is incorrect because the resistance ratio is not simply proportional to $\sqrt{d}$.. Option B is incorrect because the effect is non-linear with respect to the diameter.

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

Exam Tip: Always remember that skin effect is why stranded conductors or hollow ACSR (Aluminum Conductor Steel Reinforced) cables are used in high-voltage lines to optimize material usage and reduce effective resistance.

Examoogle · Answer

Option A: Square root of conductor diameter

Examoogle · Answer

Option B: Conductor diameter

Examoogle · Answer

Option D: None of above

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)