When current flows through a conductor, the voltage drops along the conductor. Too large a voltage drop gives dim light, poorly performing motors and unnecessary energy loss. Here are the formula, the conductivity for copper and aluminium, and the indicative limits.
Introduction
When current flows through a conductor, the voltage drops along the conductor because of the conductor's resistance. Too large a voltage drop gives dim light, poorly performing motors and unnecessary energy loss in the cable.
The formula
Calculate with the conductivity in service: κ ≈ 44.4 for copper and κ ≈ 27.8 for aluminium (Annex G of DS/HD 60364-5-52). The familiar figures 56 and 35 apply at 20 °C. For long runs and small cross-sections the voltage drop quickly becomes noticeable.
Recommended limits (Annex G)
- 01Table G.52.1 in Annex G of DS/HD 60364-5-52 recommends limits from the origin of the installation to the point of use. The annex is informative, not a Danish legal requirement.
- 02Type A — installation supplied directly from the public low-voltage network: max. 3 % for lighting and max. 5 % for other installations. This is the usual situation in a dwelling.
- 03Type B — installation with a private supply (e.g. its own transformer): max. 6 % for lighting and max. 8 % for other installations.
- 04Lighting is more sensitive than ordinary socket outlets — hence the lower limit.
The reactance term — when the cross-section becomes large
For small cross-sections, the conductor's resistance R dominates, and the simple formula above is enough. For large cross-sections (typically from around 50–95 mm² and upwards) the conductor's reactance X becomes noticeable, and the full voltage drop must be calculated with both R and X — otherwise you get too optimistic a result.
sin φ hentes ud fra cos φ: sin φ = √(1 − cos²φ). Ved cos φ = 0,9 er sin φ ≈ 0,44. Reaktansleddet betyder, at meget store kobberkabler ikke får helt så lavt et spændingsfald, som tværsnittet alene antyder — R falder med tværsnittet, men X gør det stort set ikke.
The thermal conductivity κ depends on temperature
Many tables use κ = 56 for copper and κ = 35 for aluminium, but those values apply at 20 °C. In service a loaded conductor is warm — up to 70 °C for PVC insulation — and its resistance is higher. Annex G therefore uses the resistivity in normal service: ρ₁ = 1.25 · ρ₂₀ = 0.0225 Ω·mm²/m for copper and 0.036 Ω·mm²/m for aluminium, i.e. κ = 1/ρ₁ ≈ 44.4 and 27.8. If you calculate with 56, the voltage drop comes out approx. 20 % too low. (Source: DS/HD 60364-5-52, Annex G; textbook material, Erhvervsskolernes Forlag.)
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