In a TN earthing system the cornerstone of protection against electric shock is that the protective device ‘circuit breaker’ shall not exceed it’s maximum disconnection time.
For a 230 v to earth TN system (covers both single phase and 3-phase) that is 0.4 seconds (final circuits less than or equal to 32A) see T41.1 and 5 seconds (distribution circuits and >32A) see 411.3.2.3
In order to meet those disconnection times for fault protection in a TN system a circuit breaker needs ‘X’ amount of current (Ia) …
A Type B circuit breaker is 5 x their rating ( Ia = 5 x In )
A Type C circuit breaker is 10 x their rating ( Ia = 10 x In )
A Type D circuit breaker is 20 x their rating for a 0.4 sec disconnection ( Ia = 20 x In)
A Type D circuit breaker is 10 x their rating for a 5 sec disconnection ( Ia = 10 x In )
So by using this information and Ohms Law (I = V/R) we can see that a 10 A Type B circuit breaker needs at least 50 A and we know our voltage is 230 v so the maximum resistance (impedance) would be 230 / 50 = 4.6 ohms
However because the voltage is never a constant 230v we need to make allowances for the fluctuation. Hence the new Cmin values.
The Electricity Safety, Quality and Continuity Regulations provide the value for Cmin as 0.95
So the new calculation is…
(230 x 0.95) / 50 = 4.37 ohms which is the maximum Zs for a 10 A Type B circuit breaker
Summary: The formula for the maximum Zs
Zs = (U0 x Cmin) / Ia