Originally Posted By: Dave Sherman
Nope, the math doesn't lie. 120 at angle 0 PLUS 120 at angle of 180 = 0, just as you said. Last I checked, 120 + (-120) = 0. The potential DIFFERENCE between L1 and L2 (i.e., 120 at angle 0 MINUS 120 at angle 180) is 240 volts. Don't believe me? Here:
cos(0) = 1
cos(-pi) = -1 180 degrees off
(120 * cos(0)) - (120*cos(-pi)) = 240
Yes, the polarity is opposite, which is identical to having a sinusoidal waveform which is mathematically 180 degrees off. You're right that the magnetic flux waveform in the transformer certainly didn't change phase, but the two waveforms (with respect to neutral) ARE 180 degrees out phase, nonetheless.
Not to rain on your parade but you are using the false assumption that one leg is at 180 degrees phase angle. That is not true. Since you have access to an oscilloscope, you can prove this to yourself. Use red and black leads. Attach the red lead to one end of the scope and black to the middle. Then move BOTH leads to maintain proper polarity direction. This requires moving the red lead to center tap and the black lead to the end of the coil.
Your scope will show two 120V sine waves in phase. If they were not in phase, they'd subtract from each other (magnitude wise) and cancel each other out. They are in phase and as such will add to each other (magnitude wise) and produce a 240V. When you are measuring end to end, you are not subtracting one voltage from the other.
I'm not sure why you are having a hard time understanding this as you appear to be a smart enough person with regards to the math but you don't seem to understand how to apply it properly.