# Cmin and how to use it

### Cmin

The 17th Edition of the Wiring Regulations introduced the concept of the Cmin factor.

Tables 41.3, 41.4 and 41.6 were revised to take account of the Cmin factor given in CLC/TR 50480:2011.

Cmin is the minimum voltage factor to take account of voltage variations depending on time and place, changing of transformer taps and other considerations. Also, the notes to the Tables changed in connection with maximum permitted operating temperature.

Previous maximum earth fault loop impedence values (Zs) were reduced by 5% to take into account’ voltage variations depending on time and place, the changing of transformer taps and other considerations’.

### How to use Cmin

Uo = Nominal AC rms line voltage to earth

Zs = Earth fault loop impedance

Ia = Current causing automatic operation of protective device with the stated time

Cmin = 0.95

Cmin = minimum voltage factor to take account of voltage variations depending on time and place, changing of transformer taps and other considerations.

Formula in BS 7671               Zs × Ia ≤ Uo × Cmin

Transposed                                Zs ≤ (Uo x Cmin ) / Ia

### Example

(using BS EN 60898 Type B circuit breaker values)

Ia = 160 A (Appendix 3 Fig. 3A4)

Uo = 230 V

Zs = 1.44 Ω

Cmin = 0.95

Zs = Uo / Ia

1.44 Ω = 230 V  / 160 A

Zs x Cmin = The tabulated Zs values contained in BS 7671

1.44 x 0.95 = 1.37 Ω

where:

Zs is the impedance in ohms (Ω) of the fault loop comprising:

• the source
• the line conductor up to the point of the fault, and
• the protective conductor between the point of the fault and the source.

Ia is the current in amperes (A) causing operation of the protective device within the time specified in Table 41.1 of Regulation 411.3.2.2 or, as appropriate, Regulation 411.3.2.3.Where an RCD is used this current is the rated residual operating current providing disconnection in the time specified in Table 41.1 or Regulation 411.3.2.3.

Uo is the nominal AC rms or DC line voltage to Earth in volts (V).

Cmin is the minimum voltage factor to take account of voltage variations depending on time and place, changing of transformer taps and other considerations.

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 411.4.204)
(a) Type B circuit-breakers to BS EN 60898 and the overcurrent characteristics of RCBOs to BS EN 61009-1
Rating (amperes) 3 10 32 40 80 100 125
Zs (ohms) 14.57 4.37 1.37 1.09 0.55 0.44 0.35

Extract from Table 41.3: Zs values for Type B circuit breakers. Showing the impact of Cmin on the common 32A circuit

The IET On-site Guide and IET Guidance Note 3 applies the ‘rule of thumb’ to the New Tabulated Zs figures contained in BS 7671

BS 7671 states a maximum Zs figure of 1.37 Ω for a 32 A type B circuit breaker.

The figure quoted in  both the OSG and GN3 is 1.37 x 0.8 = 1.10 Ω