the maths behind one phase of 415V 3 phase power being 240V and not whatever 415/3 is
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Think of one phase as a wave travelling through the wire. It has peaks and troughs and the voltage varies according to where you measure on the upward or downward curve.
Then think of the second phase as the exact same thing but slightly delayed. It’s just another wave travelling through the wire slightly behind the first one. And if you were to measure the voltage again you’d get the sum of the two waves at whatever point you pick.
If there was no delay between the two waves, they would both have their peaks and troughs at the exact same time and the result of a voltage measurement would be doubled.
It’s the same idea for three phases. The result is not tripled because the peaks and troughs don’t line up. They are not in-phase with each other.
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