Worked Example: Earth Fault Loop Impedance Verification for a TN-S System per BS 7671 Chapter 41

This worked example verifies that a final circuit in a TN-S earthing system achieves automatic disconnection of supply within the time required by BS 7671:2018+A3, Regulation 411.3.2.2. The verification centres on calculating the total earth fault loop impedance Z_s at the furthest point of the circuit and comparing it against the maximum permitted value from Table 41.3.

Earth fault loop impedance is a critical safety parameter. If Z_s is too high, the fault current will be insufficient to trip the protective device within the required time (0.4 s for final circuits up to 63 A), leaving the exposed-conductive-part energised at a dangerous voltage.

The task is to determine whether Z_s at the remote end of the circuit is low enough to ensure the 32 A Type B MCB disconnects within 0.4 seconds under an earth fault condition.

First, we calculate the resistance of the line conductor (R₁) and the protective conductor (R₂) at the standard reference temperature of 20°C. From BS 7671 Table I1 (Onsite Guide), the resistance per metre of 6 mm² copper conductor at 20°C is:

Resistivity of copper at 20°C:  ρ20 = 1.724 × 10&sup-8; Ω·m

For 6 mm² conductor:
  r1 = ρ / A = (1.724 × 10&supmin;&sup8;) / (6 × 10&supmin;&sup6;)
  r1 = 2.873 × 10&supmin;³ Ω/m
  r1 = 3.08 mΩ/m  (tabulated value from BS 7671 Table I1)

Since the line and PE conductors are both 6 mm² copper:

r1 = 3.08 mΩ/m  (line conductor)
r2 = 3.08 mΩ/m  (protective conductor)

(r1 + r2) at 20°C = 3.08 + 3.08 = 6.16 mΩ/m

For 25 m route length:

(R1 + R2)20°C = 6.16 × 25 / 1000
(R1 + R2)20°C = 0.154 Ω

Conductor resistance increases with temperature. During a fault, the conductor heats rapidly. We must calculate the resistance at the maximum operating temperature to determine the worst-case loop impedance. The correction factor from 20°C to the operating temperature is given by BS 7671 Regulation 411.4.4 and Appendix 14:

Temperature correction factor:
  Ct = [1 + α20 × (top − 20)]

Where:
  α20 = 0.00393 /°C  (temperature coefficient for copper at 20°C)
  top = 70°C  (maximum conductor operating temperature for XLPE 70°C cable)

  Ct = 1 + 0.00393 × (70 − 20)
  Ct = 1 + 0.00393 × 50
  Ct = 1 + 0.1965
  Ct = 1.20

This factor of 1.20 means the conductor resistance at 70°C is 20% higher than at 20°C. This is a significant increase and must not be neglected.

Apply the temperature correction factor to the 20°C resistance:

(R1 + R2)70°C = (R1 + R2)20°C × Ct

(R1 + R2)70°C = 0.154 × 1.20

(R1 + R2)70°C = 0.185 Ω

This represents the combined resistance of the line and protective conductors over the 25 m route at the worst-case operating temperature.

The total earth fault loop impedance is the sum of the external earth fault loop impedance (Z_e) provided by the electricity distributor and the internal circuit impedance (R₁ + R₂):

Zs = Ze + (R1 + R2)70°C  — (Eq. 1, BS 7671 Reg 411.4.5)

Zs = 0.35 + 0.185

Zs = 0.535 Ω

From BS 7671 Table 41.3 — Maximum earth fault loop impedance (Z_s) for Type B MCBs to BS EN 60898, the maximum permitted Z_s for a 32 A Type B MCB to achieve disconnection within 0.4 seconds is:

For a 32 A Type B MCB:

Zs (max) = 1.44 Ω  (from Table 41.3)

Our calculated Zs = 0.535 Ω

0.535 Ω < 1.44 Ω  → COMPLIANT

The calculated Z_s of 0.535 Ω is well within the maximum permitted value of 1.44 Ω. The circuit will achieve automatic disconnection within 0.4 seconds as required by Regulation 411.3.2.2.

As a supplementary check, calculate the prospective earth fault current to confirm it is sufficient to trip the MCB within the required time:

If = U0 / Zs  — (Eq. 2)

If = 230 / 0.535

If = 430 A

For a 32 A Type B MCB, the magnetic trip threshold is 5 × I_n = 5 × 32 = 160 A. Our fault current of 430 A is 2.7 times the magnetic trip threshold, confirming instantaneous tripping (typically within 10–20 ms, well within the 0.4 s requirement).

Fault current ratio:  If / In = 430 / 32 = 13.4

Type B magnetic trip range: 3× to 5× In
  Lower threshold: 3 × 32 = 96 A
  Upper threshold: 5 × 32 = 160 A

430 A > 160 A  → guaranteed instantaneous magnetic trip

The circuit is compliant with BS 7671 Chapter 41 for automatic disconnection of supply in a TN-S system. The earth fault loop impedance of 0.535 Ω provides a substantial margin below the maximum of 1.44 Ω, ensuring reliable protective device operation even with supply impedance variations.

• BS 7671:2018+A3, Regulation 411.3.2.2 — Automatic disconnection for TN systems (0.4 s for final circuits ≤ 63 A)
• BS 7671:2018+A3, Table 41.3 — Maximum Z_s values for MCBs to BS EN 60898
• BS 7671:2018+A3, Regulation 411.4.5 — Earth fault loop impedance formula
• BS 7671:2018+A3, Appendix 14 — Temperature correction for conductor resistance
• IET On-Site Guide, Table I1 — Conductor resistance per metre at 20°C
• BS EN 60898-1 — MCB characteristics (Type B: 3–5 × I_n)

Use the ECalPro Cable Sizing Calculator to verify earth fault loop impedance for your own circuits. Select BS 7671 as the standard, enter your Z_e value and cable details, and the calculator will automatically check Z_s against Table 41.3 — including temperature correction, the 80% rule, and full intermediate step reporting.