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32 — Calculators

Calculate touch voltage under fault

Under fault the enclosure is not at earth potential but at the voltage drop across the return path. That voltage stands until disconnection — and it is the reason disconnection times are limited at all.

Input

In a TN system the short-circuit current; in a TT system the operating current of the residual current device.

In a TN system the protective conductor resistance; in a TT system the earth resistance of the installation.

The usual limit for alternating voltage in dry areas. Special locations have a lower one.

Result

Touch voltage
—V
Assessment
—
Largest permissible resistance in the return pathAt this fault current.
—Ω
Use of the limit
—%

A guide, not a design to standard. We give no warranty for the correctness of the results, the applicable standards and case-by-case verification govern.

Worked example

The default case the calculator starts with, worked through once. Change the values above and it recalculates immediately.

Inputs

System earthing
TN – return through the protective conductor
Fault current
1,000 A
Resistance in the return path
0.083 Ω
Permissible touch voltage
50 V

Result

Touch voltage
83 V
Assessment
The limit is exceeded — disconnection has to occur within the required time.
Largest permissible resistance in the return path
0.05 Ω
Use of the limit
166 %

Formula

  • U_B = I_fault · R_return
  • TN: R = protective conductor resistance
  • TT: R = earth resistance of the installation
  • R_max = U_permissible / I_fault

Assumptions and standards

  • The calculation gives the voltage on the faulty equipment against reference earth while the fault persists.
  • The permissible limit depends on the location. Special environments — wet areas, agricultural premises, medical locations — have lower values.
  • The limit alone is not enough. If exceeded, disconnection has to occur within the required time; how quickly depends on the magnitude of the voltage.

Frequently asked

Why is touch voltage a bigger issue in a TT system?

Because the fault current returns through earth, and earth resistance is orders of magnitude higher than a protective conductor. A few hundred milliamperes across ten or twenty ohms already gives a dangerous voltage. That is why a residual current device is practically indispensable in a TT system.

Why is a smaller protective conductor not simply acceptable?

Because a smaller protective conductor has more resistance, so the touch voltage rises — proportionally at the same fault current. At the same time the fault current falls, because the loop becomes more resistive, and disconnection takes longer. Both effects work in the same wrong direction.

Is a brief excursion harmless?

Not as a blanket rule. The hazard depends on magnitude and duration together. That is why the rules couple them: the higher the touch voltage, the shorter the disconnection time must be. A high voltage gone in milliseconds is something else than a moderate one that stays.

Calculating is the easy part.

A formula gives you a number. Designing a plant also demands installation method, grouping, discrimination, the standards in force and a look at the installed base. That is what we take on.

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