11.1 Earth-Fault-Loop Impedance (Zs = Ze + R1 + R2)

Earth-Fault-Loop Impedance (Zs = Ze + R1 + R2)

Quick Answer: Zs is the impedance of the complete earth-fault loop. In MEN final-subcircuit teaching, Zs = Ze + R1 + R2. Ze is the external (upstream/supply) contribution; R1 is the active conductor resistance of the circuit; R2 is the protective-earthing conductor resistance. Fault current If ≈ U0 / Zs must be high enough for the protective device to disconnect within the AS/NZS 3000 time.

Why EFLI Is a Capstone Pillar

Chapter 9 explained that MEN turns an active-to-earth fault into a high-current metallic path via the protective earth, MEN link and neutral. Chapter 10 introduced prospective fault current and adiabatic conductor heating. This chapter quantifies whether that path is actually low enough for automatic disconnection.

Queensland capstone written and practical assessments treat earth-fault-loop impedance (EFLI, symbol Zs) as non-negotiable competence. Markers expect you to:

• Name the loop components.
• Apply Zs = Ze + R1 + R2 (or the equivalent measured whole-loop value).
• Relate Zs to If and to the protective device’s time–current curve.
• Compare measured Zs against maximum Zs limits for the device.

If you can size cables and still leave Zs too high, the breaker may never clear an earth fault in time — and the installation fails verification even if continuity “beeps.”

What the Earth-Fault Loop Physically Is

Picture a Class I appliance on a final subcircuit. An active conductor contacts the earthed enclosure. Fault current travels approximately as follows:

1. From the supply transformer winding (or equivalent source) out on the active path to the fault.
2. Into the enclosure and along the protective earthing conductor (R2 path) back to the earth bar.
3. Across the MEN link to the neutral bar.
4. Back to the supply on the neutral (consumer mains / network neutral contributing to Ze).

The total impedance of that closed path is Zs. Every joint, long run of thin earth conductor, high-impedance supply, or poor MEN connection increases Zs, reduces If, and delays or prevents disconnection.

Ze is not “the electrode.” Under MEN the metallic neutral return dominates the low-impedance path; electrode resistance to soil is a different quantity and must not be substituted for Ze in this formula.

Calculated Versus Measured Zs

Calculated Zs

Designers and candidates often calculate approximate R1 and R2 from conductor resistivity, cross-section and length (AS/NZS 3008 / cable data resistance values), then add a known or estimated Ze:

• R1 rises with longer active runs and smaller CSA.
• R2 rises if the PEC is long, undersized relative to the active, or poorly terminated.
• Ze is often taken from distributor advice, measurement at the origin, or conservative design assumptions.

Calculated Zs is a design tool: it helps you choose cable size and length so that expected Zs will sit below the maximum Zs for the chosen protective device before you pull cable.

Measured Zs

On verification day (linked to Section 8 testing themes), a loop-impedance tester injects a controlled current and measures the actual loop. Measured Zs includes:

• Real supply impedance at that moment.
• Every termination, switch, joint and meter path in the loop.
• Temperature effects on conductor resistance.
• Any unexpected high-resistance joints that tables never modelled.

Rule for assessors: compliance is judged on measured values against maximum Zs tables (and related Wiring Rules verification requirements), not on a neat calculation alone. Calculation that “looks fine” does not excuse a high measured reading.

Maximum Zs Tables and Disconnection

Protective devices clear faults according to their time–current characteristics. For a given In and curve (or fuse type), there is a minimum fault current that achieves disconnection within 0.4 s or 5 s (Section 11.2). Rearranged as impedance:

Zs,max ≈ U0 / If,min

where If,min is the current that just meets the required disconnection time on the device curve. Standards and manufacturer / Wiring Rules guidance present this as maximum earth-fault-loop impedance tables for common device ratings.

Exam logic:

1. Identify the protective device (In, type/curve).
2. Identify the applicable disconnection time (final ≤32 A TN themes → often 0.4 s; distribution / larger finals → often 5 s).
3. Read Zs,max for that combination.
4. Confirm measured Zs ≤ Zs,max (with any required temperature / method corrections taught in your procedures).

If measured Zs > Zs,max, possible remedies include larger conductors (especially improving R2), shorter runs, checking joints, verifying MEN integrity, or reviewing device selection — not “hoping the RCD will cover it” as a substitute for overcurrent disconnection where the Rules require automatic disconnection by overcurrent for that fault scenario.

Worked Relationship: Zs → If → Trip

Suppose a final subcircuit has measured Zs = 0.8 Ω and U0 = 230 V:

If ≈ 230 / 0.8 = 287.5 A

For a 20 A Type C MCB, that fault current is many times In. Whether it sits in the magnetic trip band and clears within 0.4 s depends on the curve — which is exactly why Zs,max tables exist. If the same circuit had Zs = 3.5 Ω, then If ≈ 66 A, which may linger in the thermal region far too long for shock-protection disconnection times.

This is why Chapter 9’s qualitative MEN story and Chapter 11’s numbers are one competence: low Zs → high If → device operates in time.

Test-Day Habits Linked to Section 8

When verifying loop impedance:

• Confirm the installation is in its intended MEN arrangement (MEN link fitted) for in-service loop measurement reflecting normal topology.
• Test at the furthest / most onerous point on the circuit (highest expected R1 + R2).
• Do not confuse earth continuity (low resistance of the PEC alone) with Zs (whole loop including Ze and R1).
• Record results against the correct Zs,max for the actual device — swapping a Type B for Type C changes the limit.
• Investigate high readings: loose earths, undersized PEC, corroded MEN link, high upstream Ze, wrong circuit tested.

Capstone Traps in This Section Alone

• Treating Ze as electrode-to-soil resistance only.
• Using R1 + R2 without Ze and calling it Zs.
• Passing a circuit because continuity is good while measured Zs exceeds Zs,max.
• Calculating If = U0 / R2 and ignoring the rest of the loop.
• Assuming RCDs replace the need for adequate Zs for overcurrent earth-fault disconnection where that method of protection applies.

Bridge Forward

Section 11.2 locks the 0.4 s and 5 s disconnection times that set which Zs,max row you use. Section 11.3 then coordinates protective-device breaking capacity (Icu) with prospective fault current (PFC) so the device that must clear the fault can interrupt it safely. Keep the formula Zs = Ze + R1 + R2 as your first line on any EFLI question.