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
Conductivity κ is approx. 56 for copper and approx. 35 for aluminium at 20 °C. For long distances and small cross-sections, voltage drop quickly becomes noticeable.
Normal
- 01NORM (table G52.1, DS/HD 60364-5-52): max. 3% voltage drop for lighting and max. 5% for other installations.
- 02Lighting is more sensitive than ordinary outlets — hence the lower 3% limit.
- 03The number "4%" is an indicative IEC example value, not the Danish G52.1 limit — use 3%/5%.
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
Danske tabeller regner ofte med κ = 56 for kobber, men den værdi gælder ved 20 °C. I drift er en fuldt belastet leder varm — op mod 70 °C for PVC-isolering — og der falder kobbers κ mod ca. 47, altså ca. 20 % højere modstand. Regner du med 56 på et kabel, der i drift er varmt, undervurderer du spændingsfaldet. Aluminium ligger på κ ≈ 35 ved 20 °C. (Kilde: DS/HD 60364-5-52, Annex G; grundbogsmateriale, Erhvervsskolernes Forlag.)
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