Zs and the use of Ohm’s Triangle

Topic Progress:

To use the Ohm’s Law triangle, we have to consider the complete circuit, which starts at the supply transformer and has a nominal voltage of 230v

Assuming this triangle represents an AC circuit, opposition to current is impedance and the total circuit impedance is called Zs.

The current (I) becomes Prospective Fault Current (Pfc). This is how much current will flow in the event of a short to
earth or between live conductors.

For example:

A lighting circuit has a R1 + R2 value of 1.7W and is connected to a TN-S supply with a Ze value of 0.2 W. What is the Pfc at the Consumer Unit and at the extremity of the circuit?

Ohm’s Law gives:

230/0.2 = 1150A at the Consumer Unit

230/1.7 = 135A at the extremity

Note – GN3 states that there is a requirement to know the Pfc at all relevant places.

The Maximum Values of Zs

Luckily, all the hard work has been done for us. Max values of Zs needed to comply with disconnection times for each type of protective device have been calculated and listed in tables in BS7671.

All we have to do is measure a value for each circuit and compare it to the tabulated values.

Remember electric cables have a resistance and it is this that we will be measuring.

Max earth-fault loop impedance (Ohms) for 230V circuits protected by miniature circuit breakers to give compliance with 0.4s disconnection time.

Maximum earth fault loop impedance (Zs) for circuit-breakers with Uo of 230 V, for operation giving compliance with the 0.4 s disconnection time of Regulation 411.3.2.2 and 5 s disconnection time of Regulation 411.3.2.3 (for RCBOs see also Regulation 411.4.9)

(a) Type B circuit-breakers to BS EN 60898 and the overcurrent characteristics of RCBOs to BS EN 61009-1
Rating (amperes) 3 6 10 16   20 25 32 40 50 63 80 100 125
Zs (ohms)     7.28   2.73   1.75   1.09   0.69   0.44  
    14.57   4.37   2.19   1.37   0.87   0.55   0.35

Note : values in this table have changed for Amendment 3 of BS7671 (indicated in red)

What is Zs?

Zs is the total impedance of the complete circuit and it is made up of:

  • The impedance of the supply cables and transformer windings, Ze
  • The resistance of our circuit line conductor, R1
  • The resistance of our circuit cpc, R2

The Rule of Thumb

Does the 80% Rule of Thumb still apply with new Amendment 3? Well, yes it does.

The Rule of Thumb errs on the side of safety by making allowances for the possibility of a smaller csa protective conductor.

For example:

A circuit has a max Zs value of 1.37Ω. The measured value of R1 + R2 is 0.92Ω and the Ze is 0.14 Ω.

Does it comply?

Rule of Thumb = 1.37 x 0.8  = 1.096 Ω

Zs 0.14 + 0.92 = 1.06Ω, which is less than 1.096, so it is ok.

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