How does the SKIN EFFECT increase the AC Resistance?

The AC resistance increase with an increase in the frequency because more charge gets concentrated near the surface of the conductor. As we go from the surface of the conductor to the center of the conductor the charge concentration decreases and becomes zero at the center of the core. The depth till the charge concentration is available or the current flows in the conductor is known as the Skin Depth. The skin depth symbol is δ.




The skin depth decrease with an increase in the frequency for a particular conductor. It depends on the frequency and the resistivity of the material. The skin depth is proportional to the frequency and inversely proportional to the resistivity.

The skin depth of different conducting materials for different frequencies is as given below.



Skin Depth Formula

We can calculate the skin depth using the following mathematical expression. The skin depth formula is as given below.




    In case of Copper: Resistivity ρ = 1.678 μΩ cm, Relative permeability μr = 1 is used
    In case of Aluminum: Resistivity ρ = 2.6548 μΩ cm, Relative permeability μr = 1.00002 is used
    In case of Gold: Resistivity ρ = 2.24 μΩ cm, Relative permeability μr = 1 is used
    In case of Silver: Resistivity ρ = 1.586 μΩ cm, Relative permeability μr = 0.998 is used
    In case of Nickel: Resistivity ρ = 6.84 μΩ cm, Relative permeability μr = 600 is used



The skin depth is maximum if the frequency is zero-The DC has zero frequency so the skin depth is maximum and the total cross-section area of the conductor carries the current hence the DC resistance is low. The AC resistance is always higher than the DC resistance. If the skin depth is larger than the radius of the wire then the AC resistance is equal to the DC resistance.

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Relationship between AC and DC Resistance

When the ac current flows in the circuit, the distribution of the current in the conductor depends on the nature of the impedance offered by the current flowing in the conductor. If the circuit is inductive or capacitive the magnetic field set up with the flow of current will oppose the main current, and thus it will offer higher impedance.   

The higher frequency current will create a strong Lorentz Force and it brings the moving charges to the outer surface of the conductor. The AC resistance of the conductor is always higher than the DC resistance of the conductor. The main reasons for this are the SKIN EFFECT and The PROXIMITY EFFECT.

The mathematical relation between AC and DC resistance is as given below.

Rac=Rdc[1+αs+αp]

Where,
Rac = The ac resistance of the conductor
Rdc    = The DC resistance of the conductor
αs,αp = Skin effect and Proximity effect factor

The skin effect is the phenomenon in which the alternating current (AC) tends to flow mainly on the surface of a conductor, rather than throughout its entire cross-section. This occurs because the electromagnetic field generated by the AC current causes the electrons in the conductor to move in a circular motion, which creates a resistance to the current flow. The deeper the current is flowing into the conductor the less field effect it will have, resulting in less current flowing in the deeper parts of the conductor.

The skin effect causes an increase in the AC resistance of a conductor because the current is not flowing uniformly throughout the entire cross-section of the conductor. The current is concentrated on the surface of the conductor, which increases the resistance of the current flow. This results in energy loss and increased heating of the conductor.

Formally, the AC resistance due to skin effect can be calculated using the following formula:

AC resistance = (2 * ρ * frequency * length) / (π * radius)

Where:

ρ is the resistivity of the conductor material
frequency is the frequency of the alternating current
length is the length of the conductor
radius is the radius of the conductor
The skin effect can be mitigated by using thicker conductors, which have a larger radius and therefore less surface area for the current to flow through. It can also be mitigated by using a conductor with a higher electrical conductivity, which means lower resistivity, as it will have less resistance to the current flow.

What Can We Do to Solve Skin Effect?

In most cases, there is no point in worrying about it when you have helpful charts and tables to select the right wire size. In fact, local regulations will likely require a minimum wire size.

There are some strategies to overcome the problem of eddy currents.

One solution is using stranded as opposed to solid core wire. For some large wires, solid core might not even be an option. The strands (even without insulation) provide a small gap in the material, preventing much of the eddy current from forming. This is the same strategy used in high-voltage transmission lines which use bundled conductors for flexibility, increased cooling with larger surface area, and the reduction of skin effect resistance.




If the strands are individually insulated, then the eddy currents will be almost entirely removed, except for a very small amount remaining in the smaller wire strands. This is the exact same reason for lamination layers found in transformer cores and motor rotors. The downside to this strategy is the higher cost of these wires.

So, in the end, this topic may not influence your designs and your practices a great deal. However, it is important to understand the physics behind the flow of electricity to know why certain regulations and operating characteristics exist and why they might be worth preventing.

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