The Adiabatic Equation Explained

The adiabatic equation is a fundamental engineering calculation mandated by BS 7671:2018+A4:2026 (Regulation 543.1.3). It proves whether a Circuit Protective Conductor (CPC), earthing conductor, or main bonding conductor has sufficient cross-sectional area to withstand the immense thermal energy released during an earth fault before the protective device (MCB/RCBO) operates.

When to bypass Table 54.7

BS 7671 provides Table 54.7 as a simplified "rule of thumb" (e.g., matching a 16 mm² line conductor with a 16 mm² CPC). However, this table is highly conservative. Utilising the adiabatic equation allows engineers to safely specify smaller protective conductors, reducing material costs and easing installation in restricted containment.

Understanding the k Value

The 'k' factor mathematically represents the thermal capacity of the conductor material (copper, aluminium, or steel) relative to the degradation temperature of its insulation.

• Thermoplastic (PVC) at 70°C: Standard Twin & Earth cable. A fault must not cause the conductor to exceed 160°C, providing a k value of 115 for copper.
• Thermosetting (XLPE) at 90°C: Standard SWA cable. XLPE insulation can withstand fault temperatures up to 250°C, providing a higher k value of 143 for copper cores, allowing for a smaller CPC under identical fault conditions.
• Steel Wire Armour (SWA): When utilising the steel armour as the sole CPC, the k value is significantly lower (typically 46 for XLPE cable), meaning the I²t energy must be rigorously checked against the armour's cross-sectional area.