Why three phases? Why not one or two or four?

Why three phases? Why not one or two or four?
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Answer :

In 1-phase and 2-phase power, there are 120 moments per second when a sine wave is crossing zero volts. In 3-phase power, at any given moment one of the three phases is nearing a peak. High-power 3-phase motors (used in industrial applications) and things like 3-phase welding equipment therefore have even power output. Four phases would not significantly improve things but would add a fourth wire, so 3-phase is the natural settling point.
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Related questions

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