What is difference between AC and DC Resistance of a conductor?

What is difference between AC and DC Resistance?

The AC resistance is always more than the DC resistance. Let us understand what is the difference between AC and DC resistance. The resistance of the conductor is inversely proportional to the cross-section area through which the current flows. The AC resistance is more than the DC resistance because the alternating current flowing through the conductor does not distribute uniformly and concentrates near the surface of the conductor and thus the effective cross-section area decrease and the resistance increase.

When the DC current flows through the conductor the total cross-section area of the conductor is utilized and thus DC resistance is less. AC and DC resistance calculation is important for the selection of the conductors or cables in view of the reduction of line loss.

The resistance of the conductor is expressed by the following formula.

R= ρL/A

Where,
ρ = Resistivity of the conductor (Ω⋅m)
L = length of the conductor(m)
A = Area of cross-section of the conductor( Sq.meter)

The resistance of the conductor calculated using the above-given formula is known as the DC resistance of the conductor. The AC resistance of the same conductor is always more than the DC resistance because of the skin effect and proximity effect. A conductor always offers higher resistance to the flow of alternating current compared to the resistance offered when direct current flows through the conductor. The effective cross-section area of the conductor reduces with an increase in the frequency due to the skin effect and proximity effect.

Ac resistance of the conductor at different frequencies

The tendency of an alternating current to flow near the surface of the conductor is known as the skin effect. As the frequency of the current increases, the current tends to flow at the outer surface of the conductor. The current density is largest at the outer surface of the conductor. Thus, the effective area of the conductor decreases when alternating current flows in the conductor, and the resistance gets increased.

The current distribution over the entire cross-section area of the conductor is not uniform when an alternating current flows through the conductor. The current density is higher at the outer surface of the conductor compared to the current density at its center. When the current enters the conductor it creates a force due to moving charge and this force brings the charges towards the surface of the conductor. The force increases with an increase in frequency.

With an increase in frequency, the charges move at a faster rate at the outer surface of the conductor; the cross-sectional area becomes smaller due to the skin effect, and the effective resistance of the conductor increases. The factors affecting the skin effect are the shape of the conductor, nature of the material, the diameter of the conductor, and the operating frequency.  

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 at 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

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.

skin depth of conductor

The skin depth decrease with an increase in the frequency for a particular conductor. The skin depth 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.

Image result for relation of the skin depth and frequency

The skin depth can be calculated using the following mathematical expression. The skin depth formula is as given below.

skin depth formula

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.

How Does the proximity Effect increase the AC resistance?

Proximity Effect

When the two nearby conductor carries a current, a magnetic field is set up around the conductor. The flux produced by one conductor gets linked to the other conductor and produces an eddy current around the conductor which results in an apparent increase in the resistance of the conductor. The phenomenon is known as the PROXIMITY EFFECT.

The current distribution in the conductor gets changed due to the proximity effect. The current tends to concentrated away from the center of the conductor. This leads to a decrease in the apparent cross-section area of the conductor.

The current distribution in the conductors when the current flows in the same direction is as given below.

proximity effect when current flow in the same direction

The current concentrate away from the center of both the conductors when the current flows in the same direction. Thus the apparent area of the conductor gets reduced and conductor resistance increase. If the frequency of the current is higher the current tends to concentrate farther from the center and the resistance of the conductor increase.  

The current distribution in the conductors when the current flows in the opposite direction is as given below.

proximity effect- when current flow in opposite direction

This case has similar effects but the current concentrates at the adjacent sides of the conductor. However, with this current, the resistance will get increased because of the reduction in the apparent area of the conductors.  

In the case of the DC, the SKIN EFFECT and PROXIMITY EFFECT are totally absent.  

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