Conductor Resistance — and the Reactance

Because it models resistance only. At unity power factor that is exactly right — the effective impedance collapses to R and the two methods agree to a fraction of a percent. But on a lagging load, reactance contributes real drop, and above about 1/0 in a steel raceway the reactance is comparable to the resistance. On 500 kcmil copper in steel conduit the reactance is nearly twice the resistance, and the K formula simply cannot see it.

The impedance magnitude √(R² + X²) is the right quantity for a bolted fault, where current is limited only by impedance. For a normal load the drop along the line is Ze = R·cos θ + X·sin θ, because only the component of current in phase with the voltage produces IR drop and only the quadrature component produces IX drop. Using the magnitude overstates drop on a real load — sometimes substantially.

No, and this catches people out. Look at the formula: Ze = R·cos θ + X·sin θ. On a small, highly resistive conductor where R greatly exceeds X, a lagging power factor reduces line drop, because the R·cos θ term shrinks faster than the X·sin θ term grows. On a large conductor where X is comparable to R, it increases it. The crossover sits around 1/0.

DC resistance at 75 °C, in ohms per 1000 ft, listed separately for coated and uncoated copper and for aluminum, solid and stranded. This calculator uses the uncoated stranded values. A good sanity check: multiply the Table 8 resistance by the conductor's circular mils and divide by 1000, and you get back the familiar K constants — 12.9 for copper and 21.2 for aluminum, for every size in the table.

Chapter 9 Table 8's note gives R₂ = R₁[1 + α(T₂ − 75 °C)], with α of 0.00323 for copper and 0.00330 for aluminum. It is worth doing: 4/0 copper is 0.0608 Ω/kFT at 75 °C but only 0.0500 at 20 °C — 18% lower. Conductors run hot when loaded, so voltage drop at full load is genuinely worse than a cold-resistance calculation suggests.

Because steel is magnetic, so it concentrates the magnetic field around the conductors and raises their inductance. Chapter 9 Table 9 lists separate reactance columns for steel and for PVC or aluminum raceway — roughly 25% higher in steel. It only matters on large conductors, where the reactance is a meaningful share of the total impedance.

Two things. It is real energy lost as heat — on the default 200 A run it is about 730 W, dissipated continuously into the raceway and the building. And it is the reason a loose connection is dangerous: the same formula applied to a half-ohm of contact resistance at 15 A gives 112 W inside a device box, which is a small heater with nothing overloaded.