The Voltage through the person.
I presume you mean the voltage
across the person? Do I therefore take it that the "I" in your "V = I x R" is the current through the person, and that the "R" is the resistance of that person's body?
...but that is not trivial.
In terms of the VD across (along the length of) any of the conductors we're talking about, 100-200 mA is totally trivial. Even if the resistance of the conductor were 5Ω (pretty unlikely), the VD would only be 0.5 - 1.0 V.
No. I will have to bow out not understanding.
Don't give up. It's actually very simple but we've all been there before and I am sure that once "the penny drops" you will wonder why it didn't drop 'years ago' ... and, apart from that, my selfish interest is that I would prefer not to have to live with the knowledge that my 'teaching skills' had failed
Let's try taking this in easy steps ...
I think you have accepted that in relation to the ('usual') type of L-E faults I have been discussing, the length and/or resistance of the extraneous-c-p are essentially irrelevant (provided, of course, that the resistance to MET is not so high as to mean that it does NOT qualify as an extraneous-c-p) - and that the extraneous-c-p is merely acting as a means of connection of a person to the MET. Do you agree?
If so, as you (maybe unwittingly!) suggested yourself, we can simplify the discussion by completely forgetting about the extraneous-c-p and, instead, assuming that the MET was conveniently placed (and touchable!) in the bathroom.
The 'touch voltage' (pd between the MET and the exposed-c-p which you are simultaneously touching) would then therefore simply be the potential difference between the exposed-c-p and the MET - which is the 'voltage drop across the resistance of the CPC when the fault current is flowing through it'.
Are you 'with me' so far? [I'll wait for an answer before continuing!]
So, finally: How is the reducing touch Voltage to <50V achieved as in the formula R = 50/Ia?
As I have said, I cannot make any sense of the implied suggestion that it does.
If the R one measures is (per 415.2.2) between the bathroom end of an extraneous-c-p and an exposed-c-p, then getting a result <50/Ia means one thing, and one thing only - namely that if a current of Ia were to pass
through the entire path one had measured (from bathroom end of an extraneous-c-p to an exposed-c-p), then the potential difference between them would be <50V. Simply Ohm's Law.
However, as I've said, try as I may, I cannot think of any credible way in which such a situation could arise. How one earth could one end up with (or even 'contrive') a situation in which Ia was flowing
through the entire path from bathroom end of extraneous-c-p to an exposed-c-p ???
In any other situation, R < 50/Ia (with R measured as described above)
does not guarantee anything. In particular, as I have illustrated, in the face of the ('usual') type of L-E fault I have been talking about (and in the absence of SB), the potential difference between extraneous-c-p and exposed-c-p (which I presume is what you mean by 'touch voltage'?) can be considerably more than 50V, even if "R" is extremely small, far below 50/Ia.
Hence, as I asked at the start of this thread, exactly what does 415.2.2 things that it achieves?
Kind Regards, John