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B9D3481E-5A88-4144-8294-127B990D0CAB.jpeg
now here is where it gets a little complicated.

depending on the other loads Rext and the resistance of the bond between E and N, the voltage of the N line can vary.
if it goes up, some of the current from Rext will pass back through the rcd and down the parallel path through Rn and Rfault SUBTRACTING from the current passing through the neutral line on the rcd.
this will INCREASE difference between Il and Ina and help the rcd to trip.
 
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Oh i like it!
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Not sure of the R bond though
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loving the diagram, much respect

As we know, N is at 0v and bonded to earth at some point in the system, either at the point of supply or further up the supply chain. this resistance can vary immensely depending on what type of supply you have.
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p.s. I am enjoying the technical chat, whilst having a beer.
certainly beats posts about peoples lights not working after they have (male chicken'd) about with them.
I am not saying I am right, just trying to put some science into the conversation so we all know what we are looking at. polite criticism is welcome, i have not done all the parallel path calculations but from what i can see, it is not as simple as Rfault must be below "x" for the rcd to stay latched.
it truly does depend on many other contributing factors.
 
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I'll take a step back and work up to James's (correct) observation.

At the tripping threshold, Rins = V (from faulted conductor to earth) / IΔN.
I.e. the resistance of faulty insulation that will just allow the tripping current to flow, equals the voltage across the faulty insulation divided by the tripping current. It is this voltage that we need to find, since we know the tripping current.

Considering first the case of an L-E fault, the voltage across the faulty insulation is the nominal supply voltage Uo (typically 230V) plus or minus its usual tolerance, minus any voltage drop in the conductors. These variable factors are typically a small fraction of Uo, therefore we can reasonably use Uo/IΔn to discover the minimum insulation resistance; it's the familiar 230/0.03=7.7kΩ and it is not going to vary much.

Considering an N-E fault instead, the voltage across the faulty insulation is now much lower than Uo because neutral is nominally at earth potential. The small voltage that does exist to drive current through the fault is the sum of various voltage drops along neutral and earthing conductors that form a loop between the fault and the point at which N and E connect. This is the origin if it is a TN-C-S supply, the substation if it is TN-S. Since the resistances of these cables and the magnitudes and directions of the currents flowing through them are unknown, possibly unknowable (noting that this might include current from other installations flowing through the DNO's cables and/or local earthing and bonding conductors) there is no predictable voltage from which to calculate the resistance.

We can merely estimate the order of magnitude, based on typical N-E voltages of a few volts when 1-2% of Uo is dropped along neutral conductors. At 2% of 230V the fault resistance would need to be lower than 153Ω to cause a trip, but with minimal load on it might be an order of magnitude or two lower still. There will be situations, as mentioned above, where even a hard short does not cause a trip because the fault loop voltage is so near zero that the resistance of the circuit conductor is sufficient to prevent 30mA flowing.
 
Let's not go back to the origin of a supply. As we know with any TN system, neutral is connected to earth, this is not what an RCD would monitor. Also Neutral is a live conductor, and will have 230V passing through it.
From the load side of the RCD is a value of R (N-E) is what I'm looking for.
153 ohms is quite low, so are you suggesting that an 200 ohm would NOT open the RCD with 30mA flowing through circuit?

I'm going to do a practical experiment on this, with some resistors that I have in my kit.

Thanks for a rather in depth reply, although I've got to keep reading it over, its rather hard to digest at 5 30 am in the morning.

Peace brothers
 
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Wear some safety glasses, a small mistake could lead to exploding resistors.
 
For a TN system it is 7667 ohms not 1667, that is for TT systems.
Where the maximum Zs value for a protective device cannot be satisfied in a TN system, Regulation 531.3. 1 permits an RCD (including an RCBO) to be used to provide automatic disconnection of the supply. Table 41.5 would therefore apply and the maximum tablulated Zs value for a 30mA RCD is 1667 ohms
 
neutral is connected to earth
Also Neutral is a live conductor, and will have 230V passing through it.

230V with respect to what? A voltage cannot 'pass through' a conductor, it is the potential between two points. Revisit PC1966's post and mine to get a clear picture of the source of the voltage that appears across the N-E fault. That will demonstrate why we need to consider the cables back to the origin and beyond, and why the minimum resistance to cause a trip cannot be predicted and could be as low as zero ohms.

Zs>7.7kΩ: RCD won't trip (at least, cannot be relied on to trip, it's allowed to trip down to 15mA)
7.7kΩ>Zs>1.7kΩ: RCD trips, touch voltage >50V so cannot be used as fault protection
Zs<1.7kΩ: RCD trips, touch voltage <50V, everyone's happy.
 
Revisit PC1966's post

Excuse me what post is that? Certainly not in this thread, and not one I have visited before.

A disconnected neutral has the potential to be live with 230V to earth.

As we all know a neutral is a live conductor.
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Zs>7.7kΩ: RCD won't trip (at least, cannot be relied on to trip, it's allowed to trip down to 15mA) 7.7kΩ>Zs>1.7kΩ: RCD trips, touch voltage >50V so cannot be used as fault protection Zs<1.7kΩ: RCD trips, touch voltage <50V, everyone's happy.

Indeed sir, but dosnt quite answer the OP.
 
Sorry, I meant James's post #19.

The neutral is a live conductor but under normal operating conditions it is near earth potential. On a single-phase system, that is the only factor that makes it a neutral, so it's only meaningful to consider Rins of a neutral conductor, when it is intact and near earth potential as intended.
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I've drawn out the voltage divider explicitly here, for the very simple case that there is one circuit on a TN-S supply with an insulation fault at the end, in either the line or the neutral. In this case we can calculate the minimum value of Rins based on the voltage at each of the two possible fault positions.
15949029072213314660556230079017.jpg
 
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