Understanding the Principles and Mathematical Relationships of Differential Protection Selection

There are no mathematical relationships. Security is selected depending on the conditions and what it is supposed to protect. It's best to take a book where the environmental conditions and the amount of protection are given. If I find it, I will provide it, if necessary, i.e. the size of the security and from what book.

is selected depending on the value of the residual current - for protection against electric shock. typically 30 mA
on the load current, but it is best (to exaggerate) e.g. 63A
selection depending on the selectivity of protection (RCD-selective)
selection depending on the nature of the power supply - 3-phase, 1-phase

The general rule is that the residual current circuit breaker (commonly known as a differential switch) is selected for the residual current value. If the switch is installed in a residential building (single-family house, apartment, etc.), its value cannot be higher than 0.03A (30mA). For industrial installations it may be higher, e.g. 0.3A (300mA).
The residual current circuit breaker is not an overcurrent or overload protection, so the current value given in the marking - e.g. 40 /0.03 refers to the current capacity of the main contacts of the circuit breaker. As written earlier, it is safer to assume it is one order higher than the expected continuous current in the installation. All this data can be read from the circuit breaker characteristics, which should be attached to it.
Moreover, you also need to know what the power supply system is like in the protected installation, because using a "differential" only makes sense in an installation separated by a PE and N cable.

There are also 100 and 200 mA residual current protection devices.

janusz7273 wrote:

There are also 100 and 200 mA residual current protection devices.

That's why I wrote: "For industrial installations it may be more, e.g. 0.3A (300mA). "
For your information, there are also circuit breakers with lower residual current values. Moreover, when selecting a switch, you should take into account the type of current that will flow through the switch - alternating sinusoidal, "half-wave" sinusoidal or rectified. I am leaving aside issues related to the selectivity of switches in series-connected circuits, etc.

What Kapas writes is all correct, I will only add that all differential switches above 30mA are intended to protect the installation against fire, not to save lives, because a current of 100mA is a lethal current for humans. The differential is only leakage protection and is not protection against short circuits or overloads, then it only acts as an ordinary switch, so it cannot be used without short circuit protection, i.e. fuses must be used at the same time, although in one case it will work if the short circuit is to the PE wire or phase. or zero but still treats it as the smoothness of the installation even though there is a short circuit.

There are also differential switches with overcurrent switches. You can recognize them by the fact that they have a characteristic written next to the max current, e.g.: 25A 0.03A - this is a differential with a maximum current of 25A, while: C25A 0.03A - is a differential with a built-in overcurrent switch that will turn it off after exceeding 25A (with characteristic C ).

Regards, Robs.

This is a detail, but just to clarify the terminology, there are no differential switches with an overcurrent switch, only overcurrent switches with a residual current element.
As for the 30mA current, as I wrote earlier, differential devices with a maximum leakage current of 30mA can be used for protection against electric shock.
When it comes to higher education, your friend is absolutely right.
Regards.

the standard for an apartment is 30mA / 40A. is completely sufficient. 30mA is a safe limit for humans, but on a well-insulated floor.

The OHMA law applies
safe voltage 50 V
resistance of the ground connection Ω

AT
I=R
In general, the maximum leakage voltage must not exceed

I only provided the basis on which the 30 mA was determined
because the theoretical resistance of a human and a current of 30 mA gives
safe voltage

When installing a differential, we must remember that it should start working at a current of 0.5ΔI, i.e. in the case of a 30 mA differential, its operating current starts from 15 mA. Of course, one will work at this value, the other will not, and therefore if we have old receivers at home with a high leakage current or overclocked contacts, which may cause the protection to operate and switch off the circuits.