Series and Parallel Transformers
Series and Parallel Connections in transformers. Observe the Dot-Polarity. When windings are in parallel the current capacity doubles. When windings are in series the voltage doubles. Wrong dot polarity in series connection just cancels the voltage and a small residual imbalance voltage remains. If wrong polarity connection is done in parallel, then a short circuit or overload may occur.
Center Tap Transformer
This is when you need to build a symmetrical dual supply like +12V and -12V supply for an opamp design.
This is also good for a two diode full wave rectifier.
But when you make a dual supply use a bridge and the center tap is ground. If you use just two diodes then one winding may be loaded more than other. That may not be good for long term transformer life. The core may get magnetized.