Skin effect of a conductor reduces with the increase in

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Option B: Resistivity of conductor material

Explanation & Concepts:
The skin effect is the tendency of an alternating current to concentrate near the surface of a conductor. The effective resistance of the conductor increases with the skin effect, which is governed by the penetration depth (skin depth, $\delta$); as the resistivity ($\rho$) of the material increases, the skin depth increases, thereby reducing the skin effect.

Working Principle: The skin effect is caused by eddy currents induced by the internal magnetic flux of the conductor. These eddy currents oppose the current flow at the center and reinforce it at the surface. The skin depth is defined as $\delta = \sqrt{\frac{\rho}{\pi f \mu}}$, where $\rho$ is resistivity, $f$ is frequency, and $\mu$ is permeability. Increasing $\rho$ increases $\delta$, leading to a more uniform current distribution across the cross-section, hence reducing the skin effect.

Key Formulas: $\delta = \sqrt{\frac{\rho}{\pi f \mu}}$ — Skin depth formula where $\rho$ is resistivity, $f$ is frequency, and $\mu$ is permeability.; $R_{ac} = R_{dc} (1 + k)$ — Relationship showing increase in resistance due to skin effect.

Key Points: Skin effect is negligible at DC ($f=0$).; High resistivity materials exhibit less skin effect than low resistivity materials.; Larger conductor diameters exacerbate the skin effect.; Magnetic materials (high $\mu$) increase the skin effect.

Advantages: Useful for high-frequency shielding applications.; Helps in designing high-frequency inductors.

Disadvantages: Increases AC resistance of transmission lines.; Leads to increased power losses in power systems.

Applications: Power transmission line design.; Radio frequency (RF) antenna design.; Coaxial cable design.

Additional Info: For copper, $\rho$ is low, leading to a significant skin effect at 50/60 Hz in large cables.. Option A (Frequency) and D (Permeability) increase the skin effect when increased, rather than reducing it.

Answer: B is correct — An increase in the resistivity of the conductor material increases the skin depth, which leads to a more uniform current distribution and consequently reduces the skin effect.

Exam Tip: Always remember the inverse relationship: If any parameter in the denominator of the skin depth formula ($f$, $\mu$) increases, the skin effect increases. If the numerator ($\rho$) increases, the skin effect decreases.

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Option A: Supply frequency

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Option C: Cross section of conductor

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Option D: Permeability of conductor material

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