Earth Fault Loop Impedance: The Calculation That Determines If Your RCD Actually Protects

Installing an RCD on a circuit is not a substitute for earth fault loop impedance verification. This is one of the most persistent misconceptions in electrical installation practice.

An RCD detects residual current — the difference between current flowing out on the line conductor and returning on the neutral. If even a small amount of current leaks to earth (typically 30 mA for personal protection), the RCD trips. This protects against electric shock from touching a live part while in contact with earth.

But consider a different fault scenario: a line conductor comes into contact with the exposed metalwork of equipment (a line-to-earth fault through the CPC). For this fault to be cleared, enough current must flow through the earth fault loop to operate the protective device within the required disconnection time. If the earth fault loop impedance is too high, the fault current is too low, and the overcurrent device does not trip.

The result: a permanent fault — energising every piece of metalwork connected to the CPC — that can persist indefinitely. This is not a theoretical problem. It's a measurable, calculable condition that every circuit must satisfy.

What is Earth Fault Loop Impedance?

The earth fault loop is the complete circuit that fault current follows during a line-to-earth fault:

1. From the supply transformer secondary (star point)
2. Through the line conductor to the point of fault
3. Through the fault itself (assumed zero impedance for a bolted fault)
4. Through the CPC (circuit protective conductor) back to the distribution board
5. Through the main earthing terminal and earthing conductor
6. Through the earth electrode and/or the supply network earth return
7. Back to the transformer star point

The total impedance of this loop is Zs:

Where:

• Ze = external earth fault loop impedance (from the supply transformer to the origin of the installation) — typically 0.2–0.8 Ω for TN-S, 0.35–0.8 Ω for TN-C-S
• R₁ = resistance of the line conductor from the DB to the fault
• R₂ = resistance of the CPC from the fault back to the DB

The prospective earth fault current is then:

Where Uo is the nominal line-to-earth voltage (230 V in the UK, 230 V in Australia, 120 V in the US).

Maximum Zs Values

BS 7671, Tables 41.2–41.4 — Maximum earth fault loop impedance

BS 7671 specifies maximum earth fault loop impedance values for each type and rating of overcurrent device, based on the required disconnection time:

Type B MCB (disconnection time 0.4s for final circuits):

Type C MCB (disconnection time 0.4s):

Note how Type C MCBs (which require 5–10× rated current to trip instantaneously) have much lower Zs limits than Type B (3–5×). This means Type C MCBs are harder to protect on long cable runs.

Worked Example

Circuit: 2.5 mm² singles in conduit, 32 A Type B MCB, 30 m cable run Ze: 0.35 Ω (TN-C-S supply, measured)

Conductor resistance at 20°C (from Table I.1): 2.5 mm² Cu = 7.41 mΩ/m

R₁ (line conductor) = 7.41 × 30 / 1000 = 0.222 Ω R₂ (CPC, assuming 1.5 mm² Cu) = 12.10 × 30 / 1000 = 0.363 Ω

Maximum Zs for 32 A Type B MCB = 1.44 Ω

0.935 Ω < 1.44 Ω — compliant.

But wait — this calculation used resistance at 20°C. Under fault conditions, the conductors heat up. BS 7671 Regulation 411.4.6 requires the calculation to account for conductor temperature at the moment of fault.

The temperature correction is:

At maximum operating temperature (70°C for PVC):

Zs(hot) = 0.35 + (0.222 + 0.363) × (1 + 0.004 × 50) = 0.35 + 0.585 × 1.20 = 1.052 Ω

Still below 1.44 Ω — compliant, but with less margin. Some engineers skip this correction and find their circuits fail verification testing.

When Zs Exceeds the Maximum

If Zs exceeds the maximum value for the overcurrent device, the options are:

1. Increase the CPC size — a larger CPC reduces R₂, which reduces Zs. Going from 1.5 mm² to 2.5 mm² CPC reduces R₂ by 40%.

2. Use a lower-rated MCB type — Type B has higher Zs limits than Type C. If the circuit doesn't need Type C trip characteristics, switching to Type B may solve the problem.

3. Add RCD protection — an RCD rated at 30 mA will trip at fault currents as low as 30 mA, regardless of Zs. This provides the required disconnection even when Zs is too high for the MCB.

4. Shorten the cable run — reducing circuit length reduces R₁ and R₂.

5. Increase the cable size — a larger cable reduces both R₁ and R₂.

The NEC Approach: Equipment Grounding Path

NEC, Section 250.4(A)(5) — Effective ground-fault current path

The NEC takes a different but equivalent approach. Section 250.4(A)(5) requires the equipment grounding conductor path to have "sufficiently low impedance to facilitate the operation of the overcurrent device." The NEC doesn't provide maximum impedance tables — instead, it relies on the installer to verify that the equipment grounding conductor is properly sized per Table 250.122 and that the circuit will clear faults.

In practice, NEC installations with metallic raceways (conduit, EMT) as the equipment grounding path have very low impedance and rarely have issues. The problem arises in long runs with wire-type grounding conductors, particularly in PVC conduit where no metallic parallel path exists.

The Australian Approach

AS/NZS 3000, Clause 5.6 — Verification of earth fault loop impedance

AS/NZS 3000 requires earth fault loop impedance verification as part of the initial verification process. The maximum Zs values are calculated from the device characteristics and the required disconnection time (0.4s for final circuits, 5s for distribution circuits).

Australia's TN-C-S (MEN) system typically provides Ze values of 0.2–0.5 Ω, giving reasonable Zs margins for most circuits. However, long runs to outbuildings, sheds, and external installations frequently exceed the limits and require supplementary RCD protection.

Practical Verification

Earth fault loop impedance is measured during the initial verification (commissioning) process using a dedicated loop impedance tester. The tester creates a momentary low-impedance fault between line and earth and measures the resulting loop impedance.

Key practical points:

1. Test at the furthest point on each circuit — the point with the highest Zs
2. Test with the circuit energised — loop impedance testers require a live circuit
3. Record the ambient temperature — measured Zs at 20°C must be corrected to operating temperature for comparison against maximum values
4. Compare against the 80% rule — many verification guides recommend that measured Zs should not exceed 80% of the tabulated maximum, to allow for temperature rise and measurement uncertainty

If a circuit fails the Zs test, the most common solution is adding a 30 mA RCD. But it's better to design the circuit correctly in the first place — RCDs add cost, add a trip point (nuisance tripping), and require periodic testing.

Design Stage Calculation

The best time to catch Zs problems is during design, not during commissioning. Before installation, calculate Zs for every circuit:

1. Obtain or assume Ze from the supply authority (UK: typically 0.8 Ω maximum for TN-S, 0.35 Ω for TN-C-S)
2. Calculate R₁ from the line conductor size and route length
3. Calculate R₂ from the CPC size and route length
4. Apply the temperature correction factor
5. Compare Zs against the maximum for the selected protective device

If Zs is marginal, consider specifying a larger CPC, a lower MCB type, or RCD protection at the design stage — not as a commissioning fix.

Related Resources

• Sayano-Shushenskaya: Earthing System Failure — How inadequate earthing contributed to a catastrophic failure
• Earthing Systems: TN-S vs TN-C-S vs MEN — Earthing architecture differences across standards
• Short Circuit Withstand: Distribution Board Feeder — Earth fault paths depend on system earthing
• View all worked examples →