Sizing a CPC — the adiabatic, rearrangedHow small can a protective conductor be?

Earlier the adiabatic equation was used to find t — how long a cable survives a given fault current. Here it's rearranged to find S — the minimum size the protective conductor has to be. Same four letters, different unknown.

S

The nominal cross-sectional area of the conductor, in mm². CSA means the copper only — never the copper plus its insulation.

I

The fault current, in amperes.

t

The operating time of the protective device, in seconds — from Appendix 3.

k

A factor for the conductor and its insulation. Not the k you used in Chapter 43 earlier — these k values come from the Tables 54.2 onward.

The worked example: is the CPC in 2.5 mm² twin & earth big enough?

The scenario, word for word:

1. Find I. Type B trips at 5 × I_n — the worst case of the 3–5 range. 5 × 20 = 100 A. You could look it up in Appendix 3 instead of calculating it; you get the same number.
2. Find t. In Appendix 3, Figure 3A4 (type B) gives the current needed to operate the device within 0.1 s and within 5 s. For a 20 A type B that is 100 A, so at 100 A it operates within 0.1 s: t = 0.1 s — well inside the 0.4 s a TN final circuit needs.
3. Find k. Go to the tables from 54.2 onward and pick the right one. Twin & earth is a multicore sheathed cable with the protective conductor incorporated in it, at an assumed initial temperature of 70 °C or greater, copper — so k = 115.

S = √(100² × 0.1) ÷ 115
S = √(10 000 × 0.1) ÷ 115
S = √1000 ÷ 115
S = 31.62 ÷ 115
S = 0.27 mm² minimum

Actual CPC in the cable = 1.5 mm²
1.5 mm² ≥ 0.27 mm² → adequate

Why the k tables don't say "twin & earth"

A fair question: why isn't there a row that just says twin & earth, the way the cable tables do? Because you might be looking for the CPC inside any multicore sheathed cable — a three-core-and-earth, for instance — and the table has to cover all of them. Read the description, not the cable name.

Chapter 54 · cross-sectional area of protective conductors · the S formula ★ Tables 54.2 onward · p.210 · k values · copper in a sheathed cable = 115 ★ Appendix 3 · Figure 3A4 · type B · currents for 0.1 s and 5 s ★ 434.5 · the adiabatic (Part 4, Part 1)