jwhit said:
. . . the reason on a 3 wire 240vac system that there's no current on the neutral . . .
There is current on the neutral, if the loads are not balanced between the two phase conductors.
Suppose, for example, you have a 3-wire circuit supplying lights. For simplicity, let us say that on Phase A (I think this is the same as your "L1") you have two fixtures, each having a single 120 watt bulb. Let us say that on Phase B (I think this is the same as your "L2") you have one fixture, and it has a single 120 watt bulb. When any single bulb is turned on, it will draw 1 amp from a 120 volt source.
If you turn on one of the Phase A lights and you turn on the Phase B light, the loads are balanced. One amp of current will flow from the source along L1, go through the Phase A light fixture, then go to the point at which the common neutrals for the fixtures are connected to L3. From there, current goes ("backwards") through the Phase B light fixture, and finally goes along L2 back to the source. There will be no current returning to the source via L3.
That's what happens on the first half-cycle. On the other half cycle, current goes from the source via L2 to the Phase B light, and follows the path I describe above, in the reverse sequence.
Now turn on the second Phase A light. Load is no longer balanced between the two phases. You will get the exact same 1 amp flowing in the exact pattern I described above. But in addition, you will get one more amp flowing from the source, through the Phase A light, and back to the source via the neutral (L3). So if you used a clamp on ammeter, you would see 2 amps on L1, 1 amp on L2, and 1 amp on L3.
jwhit said:
. . . is because the two phases are opposing each other
That is true.
jwhit said:
. . . and canceling out the voltage on the line.
I am not sure I understand what you mean here.
jwhit said:
. . . In other words one phase is at zero when the other is at full voltage.
Not true. They both hit zero at the same time, and they both hit peak values at the same time. But one is hitting a positive peak at the same time the other is hitting a negative peak. In other words, when they hit zero together, one is about to go positive and the other is about to go negative. That is what is meant by saying they are in opposition.
jwhit said:
The problem I have with this theory is L1 and L2 are not 180 degree out of phase with each other?
But L1 and L2 are indeed 180 degrees out of phase with each other. So why does the theory not work for you.
jwhit said:
Is this a split phase circuit and does it require using L1 and L3 to work? I am confused.
If you don't have the neutral wire, and if the loads are perfectly balanced (as described above), then you would not notice a problem. But lights get turned on and off all the time, so the load will not stay perfectly balanced.
In my circuit, suppose you don't use the neutral wire. Suppose that only one light is turned to the "On" position. You will not have a complete circuit, and the light bulb will not illuminate. But if you turn on all three lights, then you will get only 80 volts across the pair of Phase A lights (so they will be dim) and 160 volts across the single Phase B light (so it will be very bright, and it might explode).
The neutral wire must be present, so that it can return the unbalanced current back to the source.