One hot conductor and a neutral is called single phase; that makes complete sense. It continues to make sense with three phase power where you have three separate hot conductors. Why does the logic fall apart when you have two hot conductors? And if there is a reason why those two hot conductors are called single phase, why is the first example of a single hot and a neutral also called single phase?
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You may prefer to call it split phase. The source is one phase of the 3 phase network. There is a center tap in the transformer which is a 0 Volt or Neutral reference point. If you take a meter and measure the voltage you will get this: L1 to N = 120V and L2 to N = 120V and L1 to L2 = 240V.
Edit: assuming you are talking about North America.
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