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The adiabatic equation, and when to use itWill the CPC survive the fault?
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What it's for: the final calculation. It checks whether the CPC can carry the prospective fault current for as long as the device takes to operate. In an earth fault you might have several hundred amps in the CPC. It's a piece of copper, and it can't carry unlimited current. At some point it would melt, and that could cause a fire. After, say, 0.4 s the fuse blows and everything "chills out". The question is whether the CPC survives until then.
What is k?
k covers the thermal constraints of the conductor under fault current: its material, its insulation and how warm it already is. Some analogies:
- Running up a hill: someone in their mid-50s, a few extra pounds, not feeling their best, will take a while. Twenty years younger, they'd have scarpered up it. Same hill, different constraints.
- A CPC in twin and earth is nestled between a line and a neutral, both "cooking away" with current, so it's already warm. A CPC formed by the steel wire armour of an SWA sits round the outside in fresh air with nothing heating it. Different constraints, so different k.
- A huge plate of food: "I only ate an hour ago, I can't fit any more in." It depends on the constraints of your belly at the time.
Use Chapter 54. It gives a far wider range of k values for protective conductors. k also appears in Table 43.1, but that's for a different calculation, so don't use it for earth faults.
For a CPC in 70 °C thermoplastic twin and earth (copper), Table 54.3 gives k = 115. Underneath, it asks whether the conductor is bigger than 300 mm². If yes, use 103. A 1.5 mm² CPC is much smaller than that, so it's 115.
BS 7671 · Chapter 54 · values of k for protective conductors BS 7671 · Table 54.3 · 70 °C thermoplastic, copper: k = 115 (103 above 300 mm²)
A hypothetical: you do the sum and get 1.3 mm². You've got a 1.5 mm² CPC, so "I'm all right". Here's a full numbers example using the fuse values above.
Another example: 20 A BS 3036 fuse, 1.5 mm² T&E CPC
I = 130 A (just enough for 0.4 s, from the table above) t = 0.4 s k = 115 (Table 54.3, 70 °C thermoplastic, copper) S = √(I² × t) ÷ k = √(130² × 0.4) ÷ 115 = √(16 900 × 0.4) ÷ 115 = √6760 ÷ 115 = 82.22 ÷ 115 = 0.71 mm² (minimum) 1.5 mm² CPC ≥ 0.71 mm² ✓ the CPC survives until the fuse blows
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