Testing and verification
Calculated earth fault loop impedance
- where
- earth fault loop impedance (Ω)
- external loop impedance (Ω)
- circuit line conductor resistance (Ω)
- circuit protective conductor resistance (Ω)
Explain this equation
Estimates the earth fault loop impedance at the end of a circuit by adding the circuit's conductor resistance to the external loop impedance. Use it at design stage, or to compare with a measured value.
Z_e is the external loop impedance, the part of the loop outside the installation: supply transformer, supply cable and the supply's earth return. R1 is the resistance of the circuit's line conductor and R2 that of its protective conductor, end to end. Z_s is the total loop impedance.
Fault current flows out from the supply, along R1 to the fault, back along R2 to the main earthing terminal and then through the supply earth path. These are in series, so they add. The ≈ is there because impedance and resistance are added directly, ignoring reactance, which is reasonable for smaller cables.
Z_e of 0.35 Ω plus R1 + R2 of 0.5 Ω gives 0.85 Ω. Typical declared maximum Z_e values are 0.35 Ω for TN-C-S and 0.8 Ω for TN-S supplies.
Watch out: use R1 + R2 at conductor operating temperature when comparing with design limits. Parallel earth paths can make a measured Z_s lower than this figure.
The fault loop includes the supply path and the circuit line and protective conductors. For a small circuit where reactance is negligible, add the external impedance to the circuit resistance.
Use values on a consistent temperature basis. Compare with the relevant protective-device requirement only after confirming the applicable disconnection time and conditions.
Enter your values to see the result.
Common mistake
Treating a cold R1 + R2 as the hot design value.
Limits
Approximation; larger cables can require complex impedance. Measured parallel paths can reduce Zs: do not subtract measured Ze from measured Zs to claim a continuity-test result.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.