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There are many different connection systems (socket,plug) which are symmetrical and unpolarised such as

The Schuko connection system is symmetrical and unpolarised in its design, allowing line and neutral to be reversed. (source Wikipedia)

I have a setup which I covered in the following sketch

enter image description here

in which I desire to have a circuit, which guarantees the direction of the polarity (L and N) indifferent to the direction / polarity of the connection.

That is, I would like to ask if there is a way to make it possible that no matter if I connect A with N or A with L the outcome is always that "L is guaranteed on left cable"?

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    \$\begingroup\$ Why do you want this? It's AC, remember. How do you distinguish between L and N without a reference? \$\endgroup\$ – pjc50 Jan 23 '17 at 9:31
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    \$\begingroup\$ Connect the incoming L and N to an isolation transformer (eg 230V in, 230V out). Connect one of the output wires of the transformer to earth, that becomes your neutral lead. The other wire is live. But if you want say 3kW then you need a 3kW transformer which will be very expensive. \$\endgroup\$ – Steve G Jan 23 '17 at 9:41
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    \$\begingroup\$ If this could be done, I see no benefit. You might see a benefit (incorrectly) and this might be a better target in a response. \$\endgroup\$ – Andy aka Jan 23 '17 at 9:46
  • \$\begingroup\$ @Andyaka Knowing the polarity for sure would allow to realize a switch, that switches of L instead of else having to disconnect both cables since L and N cannot be told apart. There are surely other benefits too \$\endgroup\$ – humanityANDpeace Jan 23 '17 at 10:04
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With a 2 pin plug, and no other assumptions, no.

If you had a three pin plug, so a ground reference, then you could have some active electronics in your box labelled '?', that detected which conductor was at roughly ground potential, and which had a large voltage difference, and swapped the conductors over accordingly.

The simplest concept to imagine would be a mains operated DPDT relay, energised between N and E. If N was in fact L, then it would operate, and switch the poles over. This dumping of a few mA into the ground conductor would probably be frowned on, if not outright forbidden, by most electrical authorities, and could trip a GFI if there was one on the system, so is not a practical solution, only conceptual.

With some electronics, you could do the job properly, detecting which incoming cable had the larger swing with respect to the incoming ground.

If you had only a 2 pin plug, you may still be able to get a reasonable ground reference using a large electrode in fresh air. Its capacitance to ground would mean that usually, the detected potential (using a high impedance sensor) would be less to the actual N lead than the actual L lead coming in. However, this could be fooled if there were strong electric fields around, so is less reliable than using a ground connector.

If it really matters to you which conductor is L and which N, then that probably means you have a ground reference available. Without any sort of ground, which is N and which L is not meaningful.

You can assume that any equipment fitted with a reversible 2 pin plug does not care which pole is which. It will be safe by having 'double insulated' components, requiring at least 2 faults before any shock hazzard is created. Any 'unsafe with a single insulation fault' equipment must have a safety ground connection.

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Knowing the polarity for sure would allow to realize a switch, that switches of L instead of else having to disconnect both cables since L and N cannot be told apart.

Modern design methodology means you have to produce a design that doesn't care which wire is live or neutral and anyway, there is no guarantee that L and N don't get swapped upstream at some later date.

Plus how will you form a circuit that re-arranges an on/off switch to move from one wire to another on-the-fly?

If you want to be sure that L gets switched, use a dual switch that switches both L and N, then you can be sure of L getting disconnected.

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    \$\begingroup\$ plus, the price and complexity difference of a dual switch vs a single switch is definitely much lower than having a relay of sorts to swap the lines \$\endgroup\$ – Marcus Müller Jan 23 '17 at 10:59

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