# Why are the values of maximum earth fault loop impedance different in BS 7671 to the IET’s On-Site Guide and Guidance Note 3: Inspection & Testing?

The effect heat has on electrical circuits is an important concept for electricians to understand.

An increase in heat affects all aspects of a circuit. Temperature limits of the insulation, protective devices, switchgear, accessories, etc., can be compromised and the resistance of the conductors can increase.

Rating factors are published in BS 7671:2018+A2:2022 which enable the designer keep temperature limits in check. Theses can be found in Tables 4A1-4C6 and Tables 4D1-4J4 of BS 7671:2018+A2:2022.

This article, however, is focussing on the effect heat has on the resistivity of conductors and therefore, their resistance.

## Heat and resistance theory

**Figure 1:** A low ohm resistance meter measuring the resistance of the lamp’s element

The effect heat can have on resistance of conductors can be seen in a simple experiment.

Using a low ohm resistance meter, a resistance of approximately 70 Ω would be displayed for a 60 watt @240 V tungsten lamp at around 20 °C, if measured across the element.

Using Ohm’s law, we can see that we could expect a current of:

However, the manufacturer has stated the voltage and output wattage of the lamp for a reason. This is to enable a simple calculation of the expected current when the lamp is energized to the stated voltage.

We can see we get a different result of:

Where: |

V = Voltage in volts |

I = Current in amperes |

R = Resistance in ohms (Ω) |

P = Power in watts |

**NOTE:** The reason for using 240 V in these calculations instead of U

_{o}of 230 V is because most of these older lamps are rated at 240 V rather than 230 V.

If 230 V was applied, the power output would be 55.2 watts and draw a current of approximately 0.24 amps based on element measuring 70 Ω at 20 °C.

The reason for the difference is that the temperature change was not considered in the first calculation. The resistance was measured at 20 °C but, when the lamp is energized with 240 V, the high resistance element gets hot – very hot! In fact, some types of elements could reach a temperature of up to 3,000 °C.

It is possible to alter the 20 °C resistance measurement and predict the approximate resistance value when the lamp is operating using the following equation:

Where: |

R = Predicted final resistance_{final} |

R = Original resistance at 20 °C_{o} |

β = The temperature coefficient of resistance in ohms per degree centigrade increase (For copper, the temperature coefficient of resistance is approx. 0.00393 Ω/°C. BS 7671 uses a value of 0.004 Ω/°C, whilst tungsten is 0.0044 Ω/°C.) |

Δt = Change in temperature |

Substituting the values, we obtain a more realistic resistance reading:

And then applying Ohm’s law, we get:

This is much closer to reality. This simple experiment shows how temperature needs to be considered with any resistance measurements.

If we calculate a few other temperatures along the way and create a quick graph, we can see a very linear relationship between an increase of heat and an increase of resistance.

**Figure 2:** The linear relationship between heat and resistance

## Why are the values of maximum earth fault loop impedance (max Z_{s}) different depending on which publication you read?

You may now be able to answer this but let’s look in a bit more detail about those differences.

## Designing a circuit and calculating earth fault loop impedance (Z_{s})

BS 7671:2018+A2:2022 has tables in Chapter 41 stating max Z_{s} values for some of the most common protective devices. Tables 41.2-41.4 refer to values of impedance when the circuit is running at full capacity. This is commonly 70 °C however, some cables can run higher in certain circumstances, so it is important to understand Notes 2 and 3 below Tables 41.2-41.4 (see Figure 3).

**Figure 3:** The Notes found below Tables 41.2-41.4 in BS 7671:2018+A2:2022

These maximum Z_{s} values in Tables 41.2-41.4 of BS 7671:2018+A2:2022 are useful when designing a circuit. The current carrying capacity tables, rating factors and volt drop values in BS 7671 are all comparative in keeping safely, yet economically, within the declared maximum permitted operating temperatures of any cable or equipment. Therefore, it makes sense to list the same values assuming similar conditions in BS 7671 for comparing max Z_{s}.

Guidance on how to calculate the max Z_{s} of a circuit is not provided within BS 7671:2018+A2:2022. However, Section 7.3 of The IET’s *Electrical Installation Design Guide, 5th Edition* shows how this can be calculated and confirmed to comply with BS 7671. The IET’s *Electrical Installation Design Guide, 5th Edition* states:

"Circuits are designed to meet the shock protection requirements by limiting the earth fault loop impedances to the end of the circuit (Z_{s}) to the maximum values given in Tables 41.2 to 41.4 of BS 7671 (Z_{41})."

Where: |

Z_{41 }= The max Z_{s} as listed in Tables 41.2-41.4 of BS 7671:2018+A2:2022 |

Z_{e} = The external part of the earth fault loop path (usually controlled by the DNO/DSO) |

Z_{1} = The impedance of the line conductor of the installation |

Z_{2} = The impedance of the circuit protective conductor (cpc) of the installation. These are all measured in ohms (Ω) |

It then shows how to calculate the earth fault loop impedance and the Z_{1} and Z_{2}. The Z_{e} is usually out of the control of the designer.

The equation is shown arithmetically as:

Where: |

Z_{41} = The max Z_{s} as listed in Tables 41.2-41.4 of BS 7671:2018+A2:2022 (Ω) |

Z_{e} = The external part of the earth fault loop path (Ω) (usually controlled by the DNO/DSO) |

R"_{1} = The resistance per metre of the line conductor (Ω/m) (see Tables F.1 and F.7 of the Electrical Installation Design Guide, I1 of the On-Site Guide and B1 of Guidance Note 3) |

R"_{2 }= The resistance per metre of the protective conductor (Ω/m) (see Tables F.1 and F.7 of the Electrical Installation Design Guide, I1 of the On-Site Guide and B1 of Guidance Note 3) |

C_{r} = The correction factor for temperature (see Table F.3 of the Electrical Installation Design Guide, I3 the On-Site Guide and B3 of Guidance Note 3) |

L = The length of cable in circuit (m) |

X"_{1} = The reactance per meter of the line conductor (Ω/m) (See Table F.7 of the Electrical Installation Design Guide and Tables 4d1-4J4 of Appendix 4, BS 7671) |

X"_{2 }= The reactance per meter of the protective conductor (Ω/m) (See Table F.7 of the Electrical Installation Design Guide and Tables 4d1-4J4 of Appendix 4, BS 7671) |

Note that the temperature correction factor is only applied to the resistive part of the conductor and not the reactive component.

The heat of a conductor will have no effect on reactance. Cables under 16 mm_{2} will have negligible reactance, so for the purposes of simplicity in this article, the equation below will be used for examples:

With temperature correction = 0.35 + [(0.0302) x 1.2 x 77] = 3.14 Ω.

Without temperature correction = 0.35 = [(0.0302) x 77] = 2.68 Ω.

If our protective device had a max Z_{41} of 2.73 Ω and we didn’t adjust for temperature in our calculations for our circuit Z_{s}, then we could wrongly consider the result compliant when it may not be.

## Confirming a circuit max Z_{s} after installation

When circuits are tested, the circuit will rarely be at the max operating temperature. For initial verification, a common method is to calculate the actual Z_{s} value of circuit based on the R_{1}+R_{2} reading and a measured Z_{e} reading. This is sensible because it proves the circuit will likely be compliant before energizing and removes any possibilities of parallel paths such as metallic services or structural framework of a building which could skew the results and have a reduction effect on the Z_{s}. In this case, the conductors would have never been energized so the possibility of being at max operating temperature is unlikely to say the least!

We are therefore required to alter these values to the temperature we are testing at to ensure we are comparing the actual measurement value with the max Z_{s} of that temperature. Otherwise, we could pass an unsatisfactory circuit.

Some engineers like to do an additional live Z_{s} measurement after initial verification. This can highlight any high impedance parts of the busbar, protective devices or switchgear assemblies which may not get highlighted using a calculation method of obtaining the Z_{s} value. There are always safety precautions to consider with any live working and appropriate risk assessments and methods of operating are essential.

**Example**

The max Z_{s} of a 32 A B-type circuit-breaker to BS EN 60898 is listed in Table 41.3 of BS 7671 as 1.37 Ω.

If the measured Z_{s} on the circuit was recorded as 1.25 Ω then you could assume, possibly incorrectly, that was a pass. However, the temperature at the time of measurement was not likely to be maximum permitted operating temperature so we would need to find the maximum Z_{s} for the temperature we measured the Z_{s}.

## Using guidance in Appendix 3 of BS 7671

Appendix 3 of BS 7671 simplifies this by taking into account the increase of the conductor resistance with increase of temperature due to load current which may be used to verify compliance with the requirements of Regulation 411.4 for TN systems (TT systems generally wouldn’t comply with this without the use of residual current devices (RCDs)).

It displays an equation:

Where: |

Z_{41} = The max Z_{s} as listed in Tables 41.2-41.4 of BS 7671:2018+A2:2022 |

Z_{s}(m) = The measured impedance of the earth fault current loop up to the most distant point of the relevant circuit from the origin of the installation (Ω) |

U_{0} = The nominal AC rms line voltage to Earth (V) |

I_{a} = The current in amps (A) causing operation of the protective device within the time stated in Table 41.1 of BS 7671:2018+A2:2022 or within 5 s according to the conditions stated in Regulation 411.3.2.3 |

C_{min} = The minimum voltage factor to take account of voltage variations depending on time and place, change of transformer taps and other considerations |

0.8 = The factor to take into account the increase of resistance of the conductors with the increase of temperature due to load current |

**NOTE:** For a low voltage supply given in accordance with the Electricity Safety, Quality and Continuity Regulations (ESQCR) as amended, C_{min} is given the value of 0.95.

For the example above of a 32 A Type B circuit-breaker to BS EN 60898, applying the equation in Appendix 3 of BS 7671:2018+A2:2022 would give a max Z_{s} of:

**1.37 Ω x 0.8 = 1.096 Ω**

Therefore, the measured Z_{s} of 1.25 Ω would indicate a non-compliant circuit.

This method, incidentally, provides the same values you will find in the *On-Site Guide* and *Guidance Note 3* as these publications are designed to be used in the field so publishing design values makes little sense.

**Figure 4:** Max Z_{s} values for various circuit-breakers at ambient temp (10 °C). Guidance Note 3 (Table A5) and the On-Site Guide (B6)

## Adjusting max Z_{s} for various conductor temperatures based on ambient temperatures using Guidance Note 3

Alternatively, guidance is provided in Appendix A of *Guidance Note 3* to help calculate the max Z_{s} at a variety of temperatures.

The simplest method is shown at the end of Section A1 which explains that the correction factors in Table A7 can be multiplied by the max Z_{s} values from Tables A1-A5 in *Guidance Note 3* or B2-B6 of the *On-Site Guide* to alter the max Z_{s} for a given ambient temperature.

**Figure 5:** Table A7 of Guidance Note 3 to correct 10 values of max Zs to other temperatures

Under the notes, it shows an example for a 32 A circuit-breaker to BS EN 60898 and how to adjust the 10 °C value to 25 °C. By applying the same method as the example shown for other values of ambient temperature, a similar graph can be created which shows the same heat and resistance relationship demonstrated at the start of this article.

**Figure 6:** Table of adjusted maximum values of measured Z_{s} in ohms (Ω) using simplified correcting method from Guidance Note 3 Appendix A

**Figure 7:** Graph using simplified method of ambient temperature adjustment to maximum Z_{s} in (Ω) from Guidance Note 3 Appendix A

The graph in Figure 7 shows a little wobble through the line. This is because there has been rounding in the process here, so the accuracy is reduced.

Appendix A continues to show a more accurate method which either uses the correction factors in table A7 of *Guidance Note 3* or the correction factors in Table B2. Each table requires a different F factor as they are adjusting from different temperatures.

It displays an equation to use:

Where: |

Z_{41} = The max Z_{s} as listed in Tables 41.2-41.4 of BS 7671:2018+A2:2022 |

Z_{test} = Max Z_{s} after temperature adjustment (Ω) |

F = Temperature correction factor found in Table B3 Appendix B of Guidance Note 3 (also known as C_{r} in the Electrical Installation Design Guide), Table I3 in On-Site Guide, Guidance Note 1 |

α = Ambient temperature correction factor Table B2 Appendix B of Guidance Note 3 or Table A7 Appendix A of Guidance Note 3, Guidance Note 1 |

Z_{e} = External earth fault loop impedance (Ω) |

**Example**A 32 A Type B circuit-breaker to BS EN 60898 using Table A7 of

*Guidance Note 3*for α and a correction factor (F) of 1.25 and assuming a Z

_{e}of 0.35. The graph in Figure 9 now shows a better linear relationship.

**Figure 8:** The table of adjusted maximum values of measured Z_{s} in ohms (Ω) using a more accurate correcting method given in Appendix A of Guidance Note 3

**Figure 9:** Graph using the more accurate method of ambient temperature adjustment to maximum Z_{s} in (Ω) from Appendix A of Guidance Note 3

## Which values need to be recorded on the schedule of circuit details of the model forms?

The model form schedule of circuit details has a column number 12 labelled "Maximum permitted Z_{s} (Ω)§". In the notes at the bottom of the schedule, it explains what value to input in the column.

"§ Where the maximum permitted earth fault loop impedance value stated in column 12 is taken from a source other than the tabulated values given in Chapter 41 of BS 7671:2018+A2:2022, state the source of the data in the appropriate cell for the circuit in the ‘Remarks’, column 31, of the Schedule of Test Results."

So, by default, it is expecting the values from Tables 41.2-41.4 of BS 7671:2018+A2:2022 and would expect the testing engineer to adjust and compare their actual readings accordingly. Alternatively, you could use the values stated in *Guidance Note 3*/the *On-Site Guide* but you must clearly state which publication other than BS 7671:2018+A2:2022 you have used in the remarks column.

**Figure 10:** Model form generic schedule of circuit details from BS 7671:2018+A2:2022

**Figure 11: **Model form generic schedule of circuit details from BS 7671:2018+A2:2022

## Summary

- Increased heat in the conductor, either due to current flow or external heat application, will increase the resistance in the conductor.
- Designers need to be mindful of applying temperature correction in their calculations.
- Inspectors and testers need to be mindful of actual temperatures and apply the required factors to compensate and compare results with max permitted values carefully.
- The model form is expecting values published in Tables 41.2-41.4 of BS 7671:2018+A2:2022 and the inspector can adjust accordingly as default but does not preclude using other publications if it is clearly cited in column 31 (Remarks) on the schedule of results sheet.

### Further reading

Equation 1

- The IET Shop -
*The Handbook of Electrical Resistivity*

Equations 2, 3 and 4

- The IET Shop -
*Electrical Installation Design Guide, 5th Edition*

Equation 5

- The IET Shop -
*Requirements for Electrical Installations, IET Wiring Regulations, Eighteenth Edition, BS 7671:2018+A2:2022*

Equation 6

- The IET Shop -
*Guidance Note 3: Inspection & Testing, 9th Edition* - The IET Shop -
*Guidance Note 1: Selection & Erection, 9th Edition*

Figure 3

- BS 7671, Chapter 41, Part 4: The IET Shop -
*Requirements for Electrical Installations, IET Wiring Regulations, Eighteenth Edition, BS 7671:2018+A2:2022*

Figure 4

- Guidance Note 3, Appendix A The IET Shop -
*Guidance Note 3: Inspection & Testing, 9th Edition* - The On-Site Guide, Appendix B The IET Shop -
*On-Site Guide (BS 7671:2018+A2:2022), 8th Edition*

Figure 5

- Guidance Note 3, Appendix A The IET Shop -
*Guidance Note 3: Inspection & Testing, 9th Edition*

### Special thanks to

- Leon Markwell
- Michael Peace
- Mark Coles
- Gary Gundry.