Question

Average value of current or voltage over a half cycle can be zero also. This depends on the time interval (of course T/2) over which average value is to be found . Why?

Answer 1

It is happen due to have an average voltage of zero over half a cycle if you have a DC bias in your waveform.

In other words instead of starting at zero volts, your waveform starts rising from a point of a negative DC bias voltage, or your waveform starts falling from a point of a positive DC bias voltage.