Sorry about responding a bit late to the party, I haven’t been on-line.
Sorry if it wasn’t too clear – I will attach a few pictures to try to explain.
Firstly, if we didn’t use PME or any bonding to the ground, then each case would look like this:
View attachment 61748
In this case assuming we are say ½ way along, and the earth impedance is say 400 ohm each side of the lamppost then the potential of the ground at the point of the lamppost would be around ½ of the fault voltage – so say 115 – 120V – if we touch the lamppost – which is held at zero then we have a 120V shock hazard!
If we now bond this lamppost to the ground – say by a 100 ohm connection then the fault current would go through the 400 ohm (A) and then both the 400 ohm (B) and 100 ohm in parallel.
View attachment 61749
This time then the voltage would only be 38V or so – so a much better situation.
Obviously, there are cases where the earth impedance is lower, but then the earth rod resistance would be lower as well, but for close up situations, it’s possible to get cases which aren’t much better than no bond at all
In practice however we would usually have many similar bonds to ground similar to the picture below
View attachment 61750
In this case, each point, such as the blob in the centre has a resistance to all the earth bonds around it, the closer ones may be 70 ohm, further ones 120 ohm etc – but if we take an average of 100 ohm and there are 10 of them, then the overall is around 10 ohm; however the real advantage is the effective isolation of each point from more distant ones:
View attachment 61751
In this case each the two example points end up fairly disconnected from each other – a mini near equipotential zone – in this case the equivalent circuit would look like this:
View attachment 61752
This gives a touch voltage around 5V or so for the same fault and ground resistance as the simple examples above.
Now, as has been pointed out, these aren’t true equipotential zones as any resistance at all would give rise to a voltage drop, but this is the case throughout all of the real electrical systems – even if you use 10mm^2 to bond everything throughout a house, then there will still be some resistance, and therefore some voltage drop in the event of a fault, but the regs generally use “substantially the same potential” as an EP zone/bonding criteria.
The next issue is the loss of a PEN, so with 500W this would represent a load resistance of 100 ohm or so, our situation would be this:
View attachment 61753
Effectively there would be a potential of 230V on the body of the lamp, however with the 100 ohm earth rod, it looks like this and we would have around 115V touch potential.
View attachment 61754
Although this is no good – it is better than having no earth rod, not worse.
Obviously all the above is just an oversimplification, but it illustrates that multiple bonds to ground gives both low overall resistance to ground, plus areas that form equipotential type zones - fairly disconnected from the influences of other areas forming similar zones.