Discuss Neutral current in a single phase installation confusion in the UK Electrical Forum area at ElectriciansForums.net

Through the lamps on yellow and blue phases
if the lamps are all the same rating, theoretically all of current A would travel down this route and the system would be balanced and N current would be zero.

imagine though the lamp on blue phase blew and became open circuit.
a portion of the current would then go down the N, some from the lamp on red phase, some from lamp on yellow phase.
 
I wonder whether another mathematical way of thinking about it is helpful.
When generated 3 phase is 3 separate waveforms. They are not all positive and negative at the same time.
Divide 360 degrees by 3 = each phase is 120 degrees apart.
The current at any given phase angle is found by multiplying the current by Cosine (phase angle)

So at any given moment, a balanced 5 amp load on each phase is
5Cos(0) +
5 Cos (120) +
5 Cos (240) [or -120 normally]

= 0

The key point is that at the point one phase is positive, the other two are negative.

So while “where does the current go” is the right question, the answer is that it goes nowhere but is offset by negative currents form the other phases.
 
and they challenged me as to why therefore don’t we use six phases to be even MORE efficient.
Anyone know why? (I don’t - genuine question!)

I don't know the official answer but would guess it's practicality of not having to have 6 lines instead of 3, alternators with more complex connections, transformers with more coils / connections, isolators and switchgear not having 6 poles etc.
Not forgetting physically bigger cables due to the additional, though smaller cores.
 
I don't know the official answer but would guess it's practicality of not having to have 6 lines instead of 3, alternators with more complex connections, transformers with more coils / connections, isolators and switchgear not having 6 poles etc.
Not forgetting physically bigger cables due to the additional, though smaller cores.
I think you misunderstood me there (or more likely I did a bad job of explaining myself....) What I was referring to was simply the maths - I understand all the practical engineering reasons.

If we had a theoretical six phases then if we stick to the principle of the given formula we'd end up with..

SQRT((A^2, B^2, C^2, D^2, E^2, F^2) - (AB, AC, AD, AE, AF, BC, BD, BE, BF......)) however it doesn't work in practice.
 

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