Why isn't line to line voltage zero?

If voltage is measured relative to something. For instance, voltage-meters measure voltage differences not individual voltage levels, or by analogy altitude is measured relative to somewhere. Mount Everest is so-and-so compared to sea level. But zero compared to itself.

How come line to line voltage is not zero when both lines have the same value? For instance, a three phase three wire Y connection of 120V with an angle of 120 degrees. Line to line voltage here is $$120V \times \sqrt[]{3} \approx 208V$$ not zero.

• Because, as you state, they are out of phase. Hence they are different. For example $sin(\omega t)-sin(\omega t-180^o)=2sin(\omega t)$ – Chu Mar 15 '17 at 8:17
• @Chu, so my theory was half true, in that if the phases was lined up, the voltage would be zero? – E. l4d3 Mar 15 '17 at 9:00
• Yes, if they were in phase, the voltage difference would be zero. – AngeloQ Mar 15 '17 at 12:36

The difference between +1 and -1 is 2 yet both have the same magnitude of 1. If you connect two identical 9 volt batteries together with a single wire and measure across the unconnected terminals you might measure 0 volts or you might measure 18 volts depending on how you connected the single wire. Polarity matters and it matters in 3 phase systems just the same. As you can see, although the 3 individual phase voltages are rising and falling identically, they are displaced in time and therefore there is a voltage between any two.

Picture stolen from here

• Thanks, that made sense. The difference between the phases per time unit is always different and greater than that of the line to neutral. Didn't consider that. Thanks for the last puzzle! – E. l4d3 Mar 15 '17 at 8:57

...because direction matters AC signals are time varying and they have both an amplitude and a phase. The phase is the angle between the voltages so they are not both "the same value" at the same time.

• Thanks, that made sense. Combined with the picture Andy posted, the difference between the phases per time unit is always different and greater than that of the line to neutral. Thanks for the last puzzle! – E. l4d3 Mar 15 '17 at 8:56

The very short answer is...If there is zero volts there is zero current . So power is zero too, which is not very useful. By having a phase difference you have a voltage and so current can flow if the load allows it. Now we have voltage and current = power. Now that is useful.