Earth Fault Loop Impedance — BS 7671 vs NEC Comparison

Scenario: A TN-S installation with a 32A Type B MCB protecting a final circuit. The earth fault occurs at the far end of a 50m cable run. BS 7671 requires automatic disconnection within 0.4 seconds using earth fault loop impedance (Zs) -- and the circuit either passes or fails based on a single number. NEC uses an entirely different protection philosophy. Same fault, same building, fundamentally different engineering approaches.

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The Scenario

A single-phase final circuit in a commercial office:

• Supply: 230V single-phase, TN-S earthing system
• Protective device: 32A Type B MCB (BS EN 60898 / IEC 60898)
• Cable: 4mm2 copper, PVC insulated, in surface conduit
• Cable length: 50 metres
• Conductor resistance at 20C: Line = 0.226 Ohm, CPC = 0.226 Ohm (4mm2 CPC)
• External earth fault loop impedance (Ze): 0.35 Ohm (typical TN-S supply)
• Fault location: End of circuit (worst case)

The question: will the MCB trip fast enough to protect a person who touches an exposed conductive part during a line-to-earth fault?

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BS 7671: The Earth Fault Loop Impedance Method

Regulatory Framework

BS 7671:2018+A2, Regulation 411.4.5 requires that for TN systems, each circuit meets the condition:

Zs <= U0 / Ia

Where:

• Zs = earth fault loop impedance at the furthest point of the circuit (Ohm)
• U0 = nominal line-to-earth voltage (230V)
• Ia = current causing automatic operation of the protective device within the required time

Disconnection Time Requirements (Regulation 411.3.2)

Step 1: Calculate Zs

Zs = Ze + R1 + R2

Where:

• Ze = external earth fault loop impedance = 0.35 Ohm
• R1 = resistance of line conductor = rho x L / A
• R2 = resistance of circuit protective conductor (CPC)

At operating temperature (assuming conductor at 70C for PVC cable):

R1 at 70C = R1 at 20C x (1 + 0.004 x (70 - 20))
R1 at 70C = 0.226 x 1.20 = 0.271 Ohm

R2 at 70C = 0.271 Ohm  (same size CPC)

Zs = 0.35 + 0.271 + 0.271 = 0.892 Ohm

Step 2: Determine Maximum Permissible Zs

For a 32A Type B MCB to trip within 0.4 seconds, it must reach its instantaneous trip threshold. Type B trips at 3 to 5 times rated current. The worst case (highest Zs that still achieves 0.4s) uses the lower bound:

Ia (Type B, 0.4s) = 5 x In = 5 x 32 = 160A

From BS 7671, Table 41.3:

Maximum Zs = U0 / Ia = 230 / 160 = 1.44 Ohm

But this is the theoretical value at the conductor operating temperature. BS 7671 Table 41.3 gives the maximum Zs for a 32A Type B MCB as 1.44 Ohm.

Step 3: Verify Compliance

Calculated Zs = 0.892 Ohm
Maximum Zs   = 1.44 Ohm

0.892 < 1.44  -->  PASS

BS 7671 result: COMPLIANT. The earth fault loop impedance is well within limits. The prospective earth fault current is:

If = U0 / Zs = 230 / 0.892 = 258A

A 32A Type B MCB will trip instantaneously at 258A (well above 5 x 32 = 160A threshold), achieving disconnection in approximately 0.01 seconds -- far better than the 0.4s requirement.

What If the Cable Were Longer?

Let us find the maximum cable length for compliance:

Maximum R1 + R2 = Max Zs - Ze = 1.44 - 0.35 = 1.09 Ohm

For 4mm2 Cu PVC at 70C, (R1+R2)/m = 2 x 4.61 x 1.20 / 1000 = 0.01107 Ohm/m

Maximum length = 1.09 / 0.01107 = 98.5 metres

Beyond approximately 98m, the same circuit with the same MCB fails BS 7671 compliance. The solution would be to increase cable size, use an RCD, or install a smaller MCB.

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NEC: The Equipment Grounding Philosophy

Fundamentally Different Approach

NEC (NFPA 70:2023) does not use earth fault loop impedance calculations for compliance verification. Instead, it relies on:

1. Prescriptive equipment grounding conductor (EGC) sizing -- Table 250.122
2. Overcurrent device operating characteristics -- assumed adequate by listing/certification
3. Effective ground-fault current path -- qualitative requirement (Article 250.4)
4. Ground-fault circuit interrupter (GFCI) protection -- prescriptive for specific locations

NEC Article 250.4(A)(5) -- Effective Ground-Fault Current Path

"Electrical equipment, wiring, and other electrically conductive material likely to become energized shall be installed in a manner that creates a low-impedance circuit facilitating the operation of the overcurrent device or ground detector for a high-impedance grounded system."

This is a performance requirement, not a numerical compliance test. NEC trusts the combination of:

• Listed overcurrent devices (tested to UL 489 for circuit breakers)
• Prescriptive EGC sizing from Table 250.122
• Installation methods that maintain conductor integrity

NEC Sizing for the Same Circuit

For a 30A breaker (nearest NEC standard size to 32A):

Equipment Grounding Conductor (Table 250.122):

• For a 30A overcurrent device: minimum EGC = 10 AWG copper (5.26mm2)

Circuit conductors:

• 10 AWG copper THHN at 90C: 40A capacity (Table 310.16)
• Derated to 75C termination: 35A -- adequate for 30A

NEC does NOT require:

• Calculation of earth fault loop impedance
• Verification of disconnection time
• Prospective fault current calculation at the furthest point

Where NEC Does Calculate Fault Current

NEC requires fault current calculations only for specific purposes:

1. Available fault current marking (Article 110.24) -- at the service entrance, for equipment withstand rating, not for protective device operation speed
2. Arc-flash hazard analysis (NFPA 70E) -- a separate safety standard, not part of NEC compliance
3. Series-rated systems (Article 240.86) -- for specific equipment coordination

None of these correspond to the BS 7671 Zs verification.

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Direct Comparison: Same Fault, Two Philosophies

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When BS 7671 Catches What NEC Misses

Long Cable Runs

Consider a 150m cable run (warehouse, farm building, remote equipment):

BS 7671 calculation:

R1 + R2 at 70C = 0.01107 Ohm/m x 150m = 1.66 Ohm
Zs = 0.35 + 1.66 = 2.01 Ohm
Maximum Zs (32A Type B) = 1.44 Ohm

2.01 > 1.44  -->  FAIL

BS 7671 forces the designer to address this: increase cable size, add an RCD, or split the circuit. The calculation proves the circuit is unsafe at this length.

NEC approach:

The same circuit with a 10 AWG EGC per Table 250.122 would be NEC-compliant regardless of length. The prospective fault current at 150m would be:

Zs = 0.35 + 1.66 = 2.01 Ohm (same physics)
If = 230V / 2.01 = 114A

A 30A breaker seeing 114A will trip -- but not instantaneously. At 3.8x rated current, a Type B equivalent breaker operates in the thermal range, potentially taking 5-30 seconds. During this time, exposed metalwork sits at a dangerous touch voltage.

NEC assumes the prescriptive EGC sizing handles this, but for very long runs, the fault current may be too low for fast tripping. The GFCI requirement for specific locations (bathrooms, kitchens, outdoors per Article 210.8) provides a secondary safety net in residential and commercial installations -- but industrial circuits often lack this backup.

High External Impedance

If the supply impedance is high (Ze = 0.80 Ohm instead of 0.35 Ohm -- common in rural areas), BS 7671 immediately reveals the constraint:

Maximum R1 + R2 = 1.44 - 0.80 = 0.64 Ohm
Maximum cable length = 0.64 / 0.01107 = 57.8 metres

This severely limits cable lengths. BS 7671 catches this at the design stage. NEC does not perform this check.

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When NEC's Approach Has Advantages

Simplicity for Standard Installations

For a typical 15-20m residential circuit (the vast majority of US installations), the prescriptive approach works well:

• EGC sized per table: always adequate
• Listed breaker: always trips appropriately
• Fault current: always high enough for instantaneous tripping

The BS 7671 Zs calculation for these short circuits always passes with huge margin -- the engineering effort adds no practical safety value.

Retrofit and Existing Buildings

NEC's prescriptive approach makes compliance assessment of existing installations straightforward: inspect the EGC, verify the breaker is listed, check the wiring method. No impedance measurement is needed.

BS 7671 requires measured Zs values during periodic inspection (BS 7671 Part 6). This requires specialised test equipment and trained operatives -- adding cost and complexity to building maintenance.

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Practical Implications for Multi-Jurisdiction Engineers

1. An NEC-compliant installation is not automatically BS 7671 compliant. The EGC may be correctly sized per NEC, but the Zs at the furthest point may exceed BS 7671 limits. This is especially true for long runs.

2. A BS 7671-compliant installation always meets the NEC grounding intent -- because a circuit that passes the Zs check inherently has a low-impedance fault path.

3. For international projects, calculate Zs even if only NEC applies. It is the only way to verify that fault disconnection is genuinely fast enough. NEC's prescriptive rules are necessary but not always sufficient for long runs.

4. RCDs/GFCIs bridge the gap. A 30mA RCD on every circuit (standard practice in many IEC countries) makes the Zs limit almost irrelevant for personal protection -- the RCD trips at milliamp levels regardless of loop impedance. This is why many European countries mandate RCD protection on all circuits, effectively making the Zs calculation a backup rather than primary protection.

5. Always measure Ze on site. The external earth fault loop impedance assumed in design may differ from reality. BS 7671 requires measured verification. NEC does not -- but the physics does not care about standards compliance.

6. Temperature matters. Conductor resistance increases with temperature. BS 7671 Zs calculations must use the conductor resistance at operating temperature (70C for PVC), not the 20C value. A circuit that passes at 20C may fail at 70C. The correction factor is 1.20 for copper PVC cables.

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The Four-Standard View

BS 7671, IEC 60364, and AS/NZS 3000 are aligned on the fundamental approach -- they all require Zs verification. NEC stands alone in using prescriptive grounding rules without circuit-by-circuit impedance verification.

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Worked Example: Circuit That Passes NEC but Fails BS 7671

Circuit: 80m single-phase, 20A Type B MCB, 2.5mm2 Cu PVC, TN-S (Ze = 0.50 Ohm)

BS 7671 check:

R1 at 70C = (7.41 x 1.20 x 80) / 1000 = 0.712 Ohm
R2 at 70C = 0.712 Ohm (same CPC)
Zs = 0.50 + 0.712 + 0.712 = 1.924 Ohm

Maximum Zs (20A Type B) = 230 / (5 x 20) = 2.30 Ohm

1.924 < 2.30  -->  PASS (barely)

Now increase to 100m:

R1 at 70C = (7.41 x 1.20 x 100) / 1000 = 0.889 Ohm
R2 at 70C = 0.889 Ohm
Zs = 0.50 + 0.889 + 0.889 = 2.278 Ohm

Maximum Zs = 2.30 Ohm

2.278 < 2.30  -->  PASS (marginal -- only 1% margin)

At 105m:

Zs = 0.50 + 0.934 + 0.934 = 2.368 Ohm

2.368 > 2.30  -->  FAIL

NEC check for the same 105m circuit:

• 12 AWG THHN: 25A at 75C (adequate for 20A)
• EGC per Table 250.122: 12 AWG (for 20A OCPD)
• NEC compliance: PASS (prescriptive requirements met)

But the prospective fault current:

If = 230 / 2.368 = 97A = 4.85 x 20A

A Type B MCB operates instantaneously at 5x -- so at 4.85x, it is in the transition zone between magnetic (instantaneous) and thermal (delayed) tripping. Actual disconnection time: potentially 1-10 seconds, depending on the specific device.

The circuit passes NEC. It fails BS 7671. The physics says it is marginal.

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Related Resources

• Earth Fault Loop Impedance: The Protection Check -- Deep dive into Zs calculations
• Cable Sizing: The 50m Office Feeder -- How cable size affects loop impedance
• Earthing System Comparison: TN-S vs TN-C-S -- How the earthing system changes Zs
• Protection Coordination Calculator -- Calculate Zs, If, and disconnection times for your circuit