So...phase is really a wave relationship. And each phase is shifted 60 degrees from each other (3 phases and 6 poles, so 6*60 = 360 degrees), and this corresponds to your standard generator and how each phase is derived as it rotatesI will never understand why when 3 phase is an outlet with 3 hot wires that are out of phase and a 240 outlet is 2 hot wires that are out of phase, they call the 240 outlet single phase. That seems like it should be considered 2-phase.
If you take any single phase, when one pole is 'peaking', it is 'pushing' current 100% towards the other pole. And vice versa. This will oscillate to the point that you derive frequency (hertz), with one cycle being one full rotation. In the gif above, look at the graph of A phase (blue): you start at 0, go up to +1, back down past 0 and all the way to -1, and then you finish the A phase cycle when you hit 0 again. In the US, that's 60hz (60 cycles per second) versus 50hz in Euro and many other places. Also, if you ever spend time in transformer rooms, you'll start to notice that the sound of the 'hum' is different, due to that frequency difference that results from the difference in source generator speed. This is also how you can control the speed of AC motors using VFDs...using solid state switching to pulse at certain frequencies...before this, you had to use DC motors and various speed control strategies.
But I digress...point is, any single phase is pushing current either direction, plus or minus, at any given time (or at 0 for a literal split second). The two poles that current passes between...they aren't out of phase with each other...because they're both directly opposing each other, and aligned across the generator axis. It's like...have you ever seen two men using a buck saw? that's what single-phase power is like
Now, I was out drinking tonight, so this is probably a bad idea, but I'm gonna keep going.
Functionally, there's really only 2 differences between 120vac and 240vac in the US. One...is that we ground one leg of the 120vac as the neutral (the center tap of the transformer). It's just a reference point. Both points are still tied to the transformer, and both points are 'hot'. But...with the way we ground things, the neutral is a 'grounded' conductor. But it still carries current, and current still goes back and forth constantly at 60hz. If you ungrounded the neutral, you could totally run the system as a 120/240 isolated system (don't do this) and it would function.
240vac is just the same as as 120vac, except it uses twice the number of turns/windings on the transformer, hence double the voltage. You could, technically, ground one of those legs, but in practice it's a 120/240 center-grounded single phase system
But it's still single phase. It's derived across a single set of poles, and transmitted through a single transformer. And you could have any number of taps on the secondary side...and the current will still oscillate between any two points.
Now, 3 phase...I had a lot typed up...but it's overkill, and having to explain why they cheat on three and four wire 3 phase systems. Suffice to say, 3 phase is pulling 3 different sources from the same generator. Usually we cheat and run them sharing conductors, which really muddies the waters.
In the first gif, that's a 4-wire system. 3 phase conductors, and the other 3 tied into a single neutral. Meaning it's a Star, or Wye, config. The other is Delta, or looks like a pyramid, and can use as few as 3 wires. But regardless of the relationship they're setting up by interconnecting 3 phases, you still have 3 separate phases, because they're truly out of phase with each other.
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