In a simple DC circuit, calculating resistance is straightforward. You take the material's resistivity ($ρ$), multiply it by the conductor's length ($L$), and divide by its cross-sectional area ($A$). But high-voltage AC transmission lines operate in a different reality. The resistance you calculate for DC, often called the ohmic resistance, is just a starting point. In the AC world, the effective resistance is always higher.

This isn't because the material itself changes. Instead, two phenomena, the skin effect and the proximity effect, alter how current flows through the conductor. They conspire to reduce the effective area the current uses, which in turn drives up the resistance and, consequently, the power lost as heat.

Alternating current isn't a steady flow; it constantly reverses direction. This creates a changing magnetic field both around and within the conductor. According to Faraday's law of induction, this changing field induces small, circular currents inside the conductor itself. These are called eddy currents and they work against the main current flow at the conductor's core while reinforcing it near the surface.

We can quantify this with a parameter called skin depth ($δ$). It represents the depth from the surface where the current density falls to about 37% (or 1/e) of its value at the surface. Most of the current is confined within this thin layer.

Transmission lines don't use single conductors; they use multiple cables bundled together, often carrying different phases of AC power. When these conductors are close to one another, their individual magnetic fields interact. This interaction, known as the proximity effect, further distorts the current distribution.

If currents in adjacent conductors flow in the same direction, the current in each conductor is pushed to the side farthest from its neighbor. If the currents flow in opposite directions, the current is drawn to the sides closest to each other. In a three-phase system, the relationship is constantly changing, but the net result is always a non-uniform current distribution. This crowding further reduces the effective cross-sectional area and adds to the total AC resistance.

The final pieces of the puzzle are the material of the conductor and its operating temperature. The resistance of a metal isn't constant; it increases as temperature rises. This is because higher temperatures cause the atoms in the metal's lattice to vibrate more vigorously, making it harder for electrons to pass through. This relationship is quantified by the temperature coefficient of resistance ($\\alpha$).

To combat these effects and meet structural demands, transmission lines use specialized conductors. They are almost never simple solid wires. Instead, they are stranded to give the skin and proximity effects more surface area to work with, slightly mitigating the problem. The choice of material is also critical.

An ACSR cable is a perfect example of engineering trade-offs. Steel has much higher resistance than aluminum, but it provides the mechanical strength needed to support the cable over long spans between towers. The aluminum, which is lighter and more conductive, carries the bulk of the current, primarily in its outer layers where the skin effect concentrates it.

Calculating the true AC resistance of a transmission line, therefore, is a multi-step process. It starts with the DC resistance based on material and geometry, then applies correction factors for frequency (skin and proximity effects) and temperature. Only then can engineers accurately model power losses and design an efficient, reliable grid.