What is the function and possible applications of a center-tap primary coil transformer?
Basically, have a tap in the primary of the transformer, allows you to adjust the output voltage to possible varying conditions of input voltage. This applies, for example, to power distribution transformers, which usually have 3, 5, 7 taps and a rotary switch to select between them.
Moreover, a center tap, is often found in transformers which are used in two different line voltages. The connection between one end and the center tap corresponds to the lowest voltage (eg 120 V), while the connection between one end and the other corresponds to higher voltage (eg 240 Vac).