Active voltage drop is caused by current flowing through the resistive component of conductor impedance ($I \cdot R \cos\phi$). It is in-phase with current and dissipates real power as heat ($I^2 R$ losses).

Reactive voltage drop is caused by alternating current passing through conductor inductive reactance ($I \cdot X \sin\phi$). It arises from the time-varying magnetic field around the wire and shifts voltage phase without dissipating real power. Total voltage drop is the vector combination of both components.

A single-phase circuit consists of a line and a neutral wire. The current must travel to the load and return to the source through the neutral, covering the cable length twice (factor of $2$).

In a balanced three-phase system, the vector sum of currents in the three lines is zero, so neutral current is zero. The voltage drop of interest is the difference between line-to-line source voltage and line-to-line load voltage. Due to the 120-degree phase separation, line-to-line drop relates to line-to-neutral drop by a factor of $\sqrt{3} \approx 1.732$.

As conductor temperature rises, increased atomic vibration increases the scattering of conduction electrons, which raises resistivity. The relationship is linear over normal operating ranges:

For copper, $\alpha = 0.00393 \text{ /°C}$. Designing at 20°C when a cable runs at 90°C XLPE rating ignores a 27.5% increase in conductor resistance, which would result in under-sized cables that violate safety limits and run dangerously hot.

Skin Effect is the tendency of alternating current to flow primarily near the outer surface of a conductor. It occurs because the magnetic flux lines link the center of the conductor more tightly than the outer skin, creating higher counter-electromotive force (back-EMF) at the center. This effectively increases AC resistance ($R_{ac}$) compared to DC resistance ($R_{dc}$).

At 50/60 Hz, skin effect begins to noticeably increase resistance in conductors larger than 150 mm² (approx. 300 kcmil) and must be explicitly factored into commercial cable sizing tables.

Proximity Effect is the distortion of current density within a conductor caused by the magnetic fields of nearby current-carrying conductors. When adjacent conductors carry currents in opposite directions, their magnetic fields cause current to concentrate in the adjacent parts of the conductors. If currents flow in the same direction, current is pushed to the outer sides.

This increases local current crowding and further raises effective AC resistance. The effect depends on cable spacing, conductor diameter, and frequency, and is minimized by using compact, twisted multi-core cable configurations.

A lower power factor increases the current required to deliver the same amount of real power ($P = \sqrt{3} V I \cos\phi$). Higher line current directly increases voltage drop ($I \cdot Z$).

Additionally, inductive reactance ($X$) in cables creates a reactive drop component ($I \cdot X \sin\phi$). At lower power factors, $\sin\phi$ increases (e.g., at $\cos\phi = 0.85$, $\sin\phi = 0.53$). Since reactance drops are phase-shifted relative to source voltage, a higher inductive component aligns the load voltage drop vector directly opposite to the source voltage vector, magnifying terminal voltage reduction.

Cables carrying AC generate an alternating magnetic field. When routed inside a ferromagnetic raceway (steel conduit or cable tray), the magnetic flux lines are concentrated inside the steel walls. This increases self-inductance and mutual-inductance of the circuit.

Therefore, routing cables in steel conduit increases inductive reactance ($X$) by 20% to 30% compared to PVC or non-magnetic conduits. Cable sizing calculations must adjust the reactance coefficient based on the raceway material.

Voltage drop typically becomes the limiting factor in two scenarios:

1. Long Run Lengths: As run distance ($L$) increases, drop increases linearly. For runs exceeding 50 to 100 meters (160-330 ft), conductors that are thermally sufficient (satisfying ampacity) will often violate the 3% or 5% voltage drop threshold.
2. Low Power Factor Inductive Loads: Heavy motor starting current draws up to 6 times nominal current at a very low transient power factor (e.g., $\cos\phi = 0.35$). The transient voltage drop can exceed 10%-15%, causing starter contactors to chatter or drop out unless the cable is sized up.

NEC (Informational Notes 210.19(A) & 215.2(A)(1)): Recommends a maximum voltage drop of 3% on branch circuits and 3% on feeders, with a total cumulative drop not exceeding 5% from the service entrance to the farthest outlet.

IEC 60364-5-52 (Annex G): Suggests a maximum drop of 3% for lighting installations and 5% for other power uses (heaters, motors) when supplied from public low-voltage grids. If supplied from a private substation, these limits are extended to 6% for lighting and 8% for other uses.

Parallel runs reduce voltage drop by dividing the current ($I$) among multiple conductors, effectively reducing circuit resistance and reactance. For $n$ cables in parallel, the drop is reduced by factor $n$.

To prevent current unbalance (which causes localized overheating and unequal voltage drops), standards like NEC 310.10 require that all parallel conductors per phase must:

• Be of exactly the same length.
• Be of the same conductor material and cross-sectional area.
• Have the same insulation type.
• Be terminated in the same manner.
• Be routed in the same configuration (e.g., grouped symmetrically in non-magnetic conduits or spaced identically in tray).