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Uses the transformer's secondary coils at a 50% duty rate. Current goes through one half of the secondary at a time.
It's less likely to overheat. And it has a low parts count. However it is not the most efficient use of a transformer.
Schematic #2.
Uses the transformer secondary at 100% duty rate. Current goes through the entire secondary coil on each half of the AC power cycle.
The center tap is there in case a return path for current is needed. Which is to say, the c.t. carries current only: (a) if loads are unequal, or (b) if a load is absent on either side.
Voltage is relative. when we label a node "0V", it is done to make analysis easier. after all, the node could also be labeled "1000V", with other nodes being "1005V" and "995V" instead of "5V" and "-5V".
the 0, 6, 12 markings are done to indicate how the windings are configured -- the 0V here is again just an opinion. you can call any of the terminals 0V as long as you re-label the others (-6 0 6) or (-12 -6 0).
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