DIFFERENCE BETWEEN AC AND DC RESISTANCE

A resistance measured with steady state DC current passing between two points on an object, conductor or any material when a steady DC voltage is applied across it, is the DC resistance.  It is the opposition a material or component offers to the flow of steady direct current. DC current is solely determined by physical characteristics of the element, viz. material resistivity, its length, cross-sectional area or geometry. The resistance increases with temperature governed by its temperature coefficient. DC resistance is calculated simply as Rdc = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. 

AC resistance is defined as the resistance of a conductor or component when an alternating current flows through it. AC resistance exceeds DC resistance in conductors primarily due to uneven current distribution due to skin and proximity effects. This difference grows with frequency and impacts power system efficiency, especially in high-voltage applications like those involving CVTs and capacitors.  AC resistance (Rac), or effective resistance, accounts for opposition to alternating current, including skin and proximity effects.

The AC or DC resistance also affects semiconductors and non-conductors in similar ways. In semiconductors, essentially non-linear components, an additional phenomenon called Dynamic resistance, characteristic to their behaviour, is observed. This is beyond the scope of present discussion.

AC resistance of Conductors

AC resistance of a conductor is higher than DC resistance since alternating current is not uniform across its cross section, and concentrates near the conductor surface. Effective current-carrying area thus decreases, and consequently resistance increases. This happens due to following reasons:

1. Skin effect
2. Proximity effect

AC resistance depends on two additional factors:

• Hysteresis losses
• Eddy current losses

A copper wire 1 km in length may have Rdc ≈ 1.73 Ω, while Rac may be 1.9 Ω (10% rise from skin/proximity) at 50 Hz. If DC loss in wire is 30 W, AC loss could be 36 W, thereby causing higher temperature rise for same load.

AC resistance increases with frequency of current. AC resistance is the ratio of power loss P to the square of the alternating current ( I^`2)passing through it. AC resistance is the active part of impedance Z, the other part being reactance X, coming from capacitance and inductance.

The resistance depends on the waveform of current, since RMS value depends on it. Resistance measured with a square wave current will be different from that with sinusoidal current.

Factors affecting AC resistance 

1. Skin Effect

(i) Due conductor geometry : Skin effect causes AC to concentrate near a conductor’s surface, reducing effective area and boosting resistance. High-frequency fields induce eddy currents opposing inner flow, pushing charge to the periphery.

Factors affecting the skin effect are:

• Conductor cross section diameter / geometry,
• Nature of material,
• Conductor length
• Operating frequency.

(ii) Proximity Effect:

Proximity effect is observed between nearby conductors, where magnetic fields distort current further, crowding it to facing surfaces and elevating Rac. Unlike skin effect (frequency-driven), this depends on conductor spacing and arrangement, worsening in bundled power lines or windings.

Overall result of skin effect is Rac = Rdc[1 + αs + αp], with αs and αp as skin/proximity factors.​

2. Hysteresis Loss:

A transformer, motor an inductor has hysteresis loss in its core material, which gets reflected as AC resistance component.

3. Eddy Current:

Eddy currents in core or other conductor material add to losses.  The core could be made of iron/steel, or ferrite material. Eddy current losses in transformers / inductors could be significant part of current. Certain metallurgical reactions in metal industry use eddy currents for melting. Further, eddy currents may also be gainfully used for some applications. For example, old energy meters made use of eddy currents for their operation.

4. Frequency Dependence of AC Resistance

At DC or low AC frequencies (<50 Hz), Rac ≈ Rdc. Above 1 kHz, Rac can be double or triple of Rdc in thick conductors. At 50/60 Hz power frequencies, this increase may be 5-20% for cables. Transformers and motors have higher Rac in windings due to bundled strands.​

Copper and aluminium show similar trends, but ferromagnetic cores (e.g., steel) amplify effects.  Stranded wires / Litz wires mitigate the skin effect by equalizing paths, cutting Rac up to 50% at audio frequencies. For dielectrics in capacitors, AC resistance is tied to dissipation factor (tan δ), causing resistive losses in dielectric.

AC resistance of transformer

Consider a transformer with a load between secondary terminals. If DC resistance is measured across primary terminals, it will only show DC resistance of primary wire. However, AC resistance across same terminals will have added components from hysteresis, eddy currents as also load resistance on secondary side reflected on primary through transformer action.

Mitigation of skin effect by stranded / Litz wires:

Stranded wires are preferred for AC conductors as individual strands are twisted by design so that the strands take all possible positions along the length, thereby nullifying the skin effect on current distribution. Litz wire is a version of multistrand wire for used for AC current at high frequencies. It has individually insulated wires bunched or braided together in a uniform pattern so that each strand takes all possible positions in the cross section of the overall conductor. This design reduces AC losses in high frequency windings by circumventing the skin effect.