Cable resistance (R) and reactance (X) in voltage-drop calculations — when X may and may not be neglected

The guide on §525 — Voltage drop covers the recommended 3% and 5% voltage-drop limits and a practical rule-of-thumb formula based on resistance alone. This guide goes deeper into the question of when that simplified formula suffices and when the cable's inductive reactance must also be taken into account.

The full formula from Annex G

Annex G of IEC 60364-5-52 gives the voltage drop as a function of both the resistance R and the reactance X of the cable per unit length:

ΔU = b × Ib × L × (R cos φ + X sin φ)

where b = 2 for a single-phase circuit and b = √3 for a three-phase circuit, Ib is the load current, L is the cable length, R and X are the resistance and reactance per unit length of the cable respectively, and φ is the phase angle between voltage and current of the load.

Why R dominates for small cross-sections

The ohmic resistance R of a conductor is inversely proportional to its cross-section (R = ρ / A): the larger the cross-section, the smaller the resistance per unit length. The inductive reactance X of a cable at 50 Hz, by contrast, depends mainly on the geometric layout of the cable (spacing between conductors, number of cores) and changes relatively little with cross-section — a commonly used practical value for the reactance of low-voltage cables is on the order of 0.08 Ω/km per phase, regardless of whether the cross-section is small or medium-sized.

The result is that at small cross-sections R is much larger than X, so the contribution of the X sin φ term to the total voltage drop is negligibly small. As the cross-section increases, R decreases while X stays roughly constant, shifting the ratio between the two and giving the reactance an increasingly larger share of the total voltage drop.

The threshold: 50 mm² copper / 70 mm² aluminium

According to Annex G of IEC 60364-5-52, the reactance may be neglected for cables with a cross-section of up to and including 50 mm² for copper and up to and including 70 mm² for aluminium — in that range, the simplified formula with only the resistive term suffices:

ΔU (%) = (b × Ib × cos φ × L × 100) / (γ × A × U₀)

where γ is the conductivity of the material at operating temperature and A is the cross-section in mm². Above those cross-section thresholds, the full formula with both R and X must be used, because omitting the reactance term then leads to a noticeably too-low calculated voltage drop.

Why this matters in practice

For a large-consumer connection, a long feeder cable to a sub- distribution board, or a cable to a charging plaza with multiple EV chargers, a cross-section of 70, 95, 120 mm² or larger is often used. At those cross-sections, the cable is above the 50 mm² threshold (for copper), and the simplified R-only formula yields a voltage drop that comes out lower than the actual value — with the risk that an installation appears on paper to stay within the 5% limit, while the actual voltage drop exceeds it.

Practical relevance

When sizing cables with a cross-section around or above the 50/70 mm² threshold, it is important not to blindly carry over the simplified rule-of-thumb formula from an earlier, smaller sizing exercise, but to use the full R and X values from the cable specification or from Annex G of IEC 60364-5-52. For circuits with a low power factor (cos φ), such as certain motor-starting circuits, the X sin φ term also carries extra weight, even when the cross-section is just below the threshold.

Common mistakes

Applying the simplified R-only formula to a cable above 50 mm² copper (or 70 mm² aluminium) — this underestimates the actual voltage drop because the reactance contribution is left out.
Assuming reactance scales proportionally with cross-section the way resistance does — X changes only slightly with cross-section in approximation, while R decreases inversely with it, so the ratio between the two actually shifts at larger cross-sections.
Ignoring the reactance term for a low-cos φ load (for example a starting motor) — the X sin φ contribution is larger the larger sin φ is, so reactance carries more weight precisely at a low cos φ than at a load with cos φ close to 1.
Using generic R and X table values without accounting for the cable construction (single-core vs. multi-core, conductor spacing) — the exact reactance value depends on the geometry of the cable; for an accurate calculation, the cable manufacturer's data or the tables in Annex G apply.