Installation design
TT resistance and residual-current relationship
- where
- electrode and protective-conductor resistance (Ω)
- RCD rated residual operating current (A)
- touch-voltage limit (V)
Explain this equation
Checks earth electrode resistance against an RCD's operating current in a TT system, so that touch voltage stays within limits during an earth fault. Use it when designing or testing a TT installation.
R_A is the earth electrode resistance plus the resistance of the protective conductor to the exposed metalwork, in ohms. IΔn is the RCD's rated residual operating current in amperes. U_L is the touch-voltage limit, commonly 50 V. The calculator gives R_A × IΔn, the arithmetic maximum R_A for the limit, and the margin left.
When the residual current IΔn flows through R_A, the exposed metalwork rises to R_A × IΔn above true earth, by Ohm's law. Keeping this under U_L means the RCD trips before the metalwork reaches a dangerous voltage.
100 Ω with a 30 mA RCD gives 3 V, far below 50 V. The arithmetic maximum for 30 mA at 50 V is about 1667 Ω, but practical electrode values should be far lower, because high readings tend to be unstable.
Watch out: enter 30 mA as 0.03 A. The arithmetic maximum is not a target; RCD operation and disconnection time must also be verified.
This relationship coordinates a TT protective arrangement with the applicable touch-voltage limit. Convert milliamps to amps before multiplying resistance by residual operating current.
A numerical result below the limit is only one part of the assessment. Reliable electrode performance, RCD selection and required disconnection time must also be addressed.
Enter your values to see the result.
Common mistake
Treating 30 mA as 30 A, or assuming a high calculated maximum is a good electrode design.
Limits
Enter the applicable touch-voltage limit. The arithmetic maximum RA is not a recommended electrode target or a complete compliance check. Verify RCD operation and disconnection time separately.
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.