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Updated: housekeeping and minor corrections
Updated: Replaced logic train with radian pulse control for synchronous cyclics. This stuff doesn't really matter, it's there just so you don't have to manually cycle the loads. Current config should stay synced to zero point crossings, but it may drift after a few hundred cycles. Part of the challenge in the more academic displays within the EveryCircuit interpreter is working around the universal assumption that all ICs should approximate real world components. In this case, we must take advantage of the internal clock of the software for synchronous control(every timing controlled device that doesn't use an in-circuit trigger or sync) that is still flexible. I digress; this is at the edge of the looking glass and has absolutely nothing to do with the context, it's just something worth remembering. This far, the current version should be the most stable and clear.
(The two relays and logical inputs are a proxy to manually changing the loads. They will cycle the dynamic load [orange] between three ratios. Watch the blue plot to see e how this changes the dynamic load on the neutral.)
This practical demonstration shows how a three wire (common neutral) network operates; with a strong focus on current vs purely resistive load variance. Blue is neutral current, green is current for a fixed load of 50Ω, orange is current with a proportionately cycling value (ratios of 1:1, 2:1, and 1:2 against the static load [green]).
It is absolutely critical that three wire networks like this consist of two isolated loads driven by ∅0/∅180, which is easily created with a balanced secondary center tap on the transformer, as shown. This is common of residential supply in the US; your home is likely supplied with single phase 240, with a center tap neutral for two 120 phases. If you try to do this with one phase, you will effectively double the neutral current (constructive interference of the wave function) along with causing a number of potential hazards. While it may 'work', the neutral load will be very high, which is one of the aforementioned potential hazards.
With a perfectly balanced load, the neutral carries zero current. Effectively, the current from each leg/phase destructively interferes.
When the loads are NOT balanced, the neutral carries the divisive current. This is fairly common and acceptable practice to split a twin Edison or similar outlet into two 15A supplies on dedicated breakers(legs, antiphase).
I typed this up fairly quickly, please comment if there is an error.
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