When measuring earth fault loop impedance (Zs) on-site with a multi-function tester (MFT), the measured value cannot be compared directly against the maximum Zs tables in BS 7671 without temperature correction. Understanding the physical derivation of the 0.8 multiplier, the Cmin factor, and when to apply exact temperature correction ensures protective devices operate within mandatory disconnection times.
The Physics: Conductor Temperature & Resistance
Copper conductors exhibit a positive temperature coefficient of resistance (α20 = 0.00393 / °C per BS EN 60228 / IEC 60228, commonly rounded to 0.004 / °C in IET guidance). As cable core temperatures rise under operational load and fault currents, conductor resistance increases predictably:
- On-Site Dead Testing: Conducted at ambient temperature (typically 10°C to 20°C) when cables are cold and carrying zero current.
- Maximum Continuous Operating Conditions: Thermoplastic (PVC) 70°C insulation operates up to 70°C; Thermosetting (XLPE / LSOH) 90°C insulation operates up to 90°C.
Crucially, external supply loop impedance (Ze) does not change with internal building cable temperature. Only the internal circuit conductors (R1 + R2) rise from ambient to operating temperature. Treating the entire Zs loop as rising by 20% is physically inaccurate:
| Insulation Type | Max Operating Temp (θmax) | Resistance Multiplier [1 + α20(θmax − 20)] | Reciprocal (1 / Multiplier) | Rule-of-Thumb Factor |
|---|---|---|---|---|
| Thermoplastic (PVC) | 70°C | 1 + 0.00393 × 50 = 1.1965 (≈ 1.20) | 1 / 1.20 = 0.833 | 0.80 (80%) (Conservative site rule) |
| Thermosetting (XLPE)* | 90°C | 1 + 0.00393 × 70 = 1.275 (≈ 1.28) | 1 / 1.28 = 0.781 | 0.78 (78%) (0.80 is non-conservative!) |
*Note on Regulation 512.1.5: If thermosetting (90°C) cable is connected to standard switchgear terminals rated for 70°C, it must be sized to 70°C current-carrying capacity, in which case the 70°C multiplier (0.80) applies.
The Cmin Factor (0.95) & Tabulated Values
The maximum Zs tables in BS 7671 (Table 41.2 for fuses at 0.4s, Table 41.3 for MCBs/RCBOs at 0.4s, and Table 41.4 for 5s disconnection) are calculated at the conductor's maximum operating temperature (70°C) using the formula:
BS 7671 Formula (Regulation 411.4.5 Note 2 & Appendix 3):
Zs ≤ (U0 × Cmin) / Ia
Where U0 = 230 V, Cmin = 0.95 (minimum voltage factor accounting for grid voltage fluctuations under ESQCR), and Ia is the tripping current.
For a standard 32 A Type B MCB (instantaneous trip Ia = 5 × In = 160 A):
Zs(max) = (230 V × 0.95) / 160 A = 218.5 / 160 = 1.37 Ω
(Prior to Amendment 3 of the 17th Edition, Cmin was omitted, giving 230 / 160 = 1.44 Ω. Always verify your instrument is calibrated to current BS 7671 tables.)
The 80% Rule of Thumb (Appendix 3)
Because on-site testing occurs when circuits are de-energised and cold, BS 7671 Appendix 3 establishes the operational rule of thumb:
Appendix 3 Verification Rule:
Zs(measured) ≤ 0.8 × Zs(tabulated)
For a 32 A Type B MCB: 1.37 Ω × 0.8 = 1.10 Ω. If the measured loop impedance is ≤ 1.10 Ω, compliance with Table 41.1 disconnection times is guaranteed without further calculation.
What to Do if Measured Zs is Between 80% and 100%
If your meter reads 1.20 Ω on a 32 A Type B circuit (exceeding the 1.10 Ω site limit, but below the tabulated 1.37 Ω maximum),do not immediately fail the circuit. The 0.8 multiplier assumes worst-case ambient temperatures (down to 10°C) and full temperature rise.
Under IET Guidance Note 3 (GN3) and Appendix 14, apply the exact temperature correction formula to calculate the actual operating loop impedance:
GN3 / Appendix 14 Exact Temperature Correction Formula:
Zs(operating) = Ze + (R1 + R2) × [(230 + θmax) / (230 + θtest)]
Where θmax = 70°C (or 90°C for XLPE) and θtest is the ambient temperature measured during the test.
Worked Example: Measured Zs = 1.20 Ω at 20°C
- Measured supply loop impedance: Ze = 0.35 Ω
- Measured circuit resistance: (R1 + R2) = 0.85 Ω (at 20°C test ambient)
- Temperature correction factor: (230 + 70) / (230 + 20) = 300 / 250 = 1.20
- Corrected operating circuit resistance: 0.85 × 1.20 = 1.02 Ω
- Corrected operating loop impedance: Zs(operating) = 0.35 + 1.02 = 1.37 Ω
- Verdict: 1.37 Ω ≤ 1.37 Ω tabulated limit → PASS.
Supplementary RCD Protection & Limitations
Where an existing circuit cannot meet the maximum Zs disconnection times even after exact calculation, Regulation 411.4.4 and Regulation 411.4.5 permit an RCD to provide fault protection on TN systems. In this case, the condition to be satisfied is Zs × IΔn ≤ U0 × Cmin. For a 30 mA RCD, this yields a theoretical limit of 7,283 Ω.
Safety Warning: Relying on an RCD for fault protection under Regulation 411.4.5 does not waive overcurrent protection requirements. The circuit breaker or fuse must still provide overload protection (Reg 433.1) and satisfy thermal constraints under the adiabatic equation (Reg 543.1.3: k²S² ≥ I²t).