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A 10 kW load on a 230 V TN-S system

1 · Design current
Ib = P ÷ V
Ib = 10 000 ÷ 230
Ib = 43.48 A   (the full load current — everything on at once)

2 · Protective device
The rule:  Ib ≤ In
The next size up from 43.48 A is In = 50 A, type B circuit breaker

3 · Disconnection time
Final circuit over 32 A supplying only fixed equipment
→ Reg 411.3.2.3: up to 5 seconds (TN)
(If the cooker control unit has a socket-outlet, it's a ≤ 63 A
circuit with a socket → Table 41.1, 0.4 s.)

4 · Maximum Zs
Table 41.3, type B, 50 A (one value for both times, Reg 411.4.202)
0.87 Ω tabulated (circuit in use)

5 · What you should measure on a new circuit
0.87 × 0.8 = 0.70 Ω   (or read it straight from OSG Table B6)

6 · Fault current needed to trip it
Type B = 5 × In (worst case)
50 × 5 = 250 A
✓If the Zs of that purple fault path in service does not exceed 0.87 Ω (0.70 Ω measured on the new, cold circuit), the breaker will operate inside the permitted disconnection time, and ADS is achieved. That's the entire chain, in one sentence.
A reality note on Ib. 43.48 A assumes every ring, the grill and the oven all running flat out at once — a Christmas dinner, not a Tuesday. In real design you'd apply diversity (maximum demand), which is why the On-Site Guide's Appendix A will happily let you put a 15 kW domestic cooker on a 32 A breaker. That's a later module.

Ib ≤ In · device rating must be at least the design current 411.3.2.3 · 5 s (TN) · or Table 41.1, 0.4 s, with a socket on the control unit Table 41.3 · 0.87 Ω On-Site Guide · Appendix A · diversity

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