What is the relationship between skin depth and AC resistance?

In summary, skin depth is a measure of how deep an AC can penetrate into a conductor and is dependent on the frequency and conductivity of the material. It can be calculated using the formula δ = √(2ρ/μω) and has an inverse relationship with AC resistance. Skin depth plays an important role in the performance of electrical systems, particularly in high-frequency applications, and can be controlled by adjusting frequency, conductivity, and conductor geometry.
  • #1
Callum Plunkett
27
8
Homework Statement
At 1 kHz, the skin depth in copper is 2 mm. Determine the a.c. resistance
at 500 kHz and at 10 MHz of 20 cm lengths of copper conductors having
the following cross sections:
(a) round section 20 mm2
(b) square section 20 mm2
(c) rectangular section 1 mm × 20 mm
Take the conductivity of copper as 5.8 × 107 Sm–1
Relevant Equations
Rac=0.25(1+D/s)Rdc
Untitled.png
 
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  • #2
Rdc is not correct. Take A=20/10^6 m^2 [in sqr.m not in sqr.mm]
and δ500kHz=0.0894 mm [2*√(1/500)] not 0.2*√(1/500)
 
Last edited:
  • #3
Thank you for the help! much appreciated.
 

What is skin depth?

Skin depth is a term used to describe the depth at which an alternating current (AC) signal penetrates into a conductor. It is a measure of how far an AC signal can travel through a material before its amplitude decreases significantly.

How is skin depth calculated?

Skin depth is calculated using the formula δ = √(2ρ/ωμ), where δ is the skin depth, ρ is the resistivity of the material, ω is the angular frequency of the AC signal, and μ is the permeability of the material. This formula takes into account the electrical and magnetic properties of the material.

What factors affect skin depth?

The skin depth of a material is affected by several factors, including the frequency of the AC signal, the resistivity and permeability of the material, and the temperature of the material. Higher frequencies, lower resistivities, and higher temperatures all result in shallower skin depths.

What is the relationship between skin depth and AC resistance?

The skin depth of a material is directly related to its AC resistance. As the skin depth decreases, the AC resistance increases. This is because a shallower skin depth means that the AC signal has to travel through more material, resulting in more resistance.

Why is skin depth important in AC circuits?

Skin depth is important in AC circuits because it affects the flow of current and the amount of resistance in a conductor. It is especially important in high-frequency circuits, where the skin depth can be very small and can significantly impact the performance of the circuit.

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