Q1: The average value of the half-wave rectified output voltage is approximately __________ of V_p.

ANS:A - 31.8%

We just have Vp, or Vmax (Vm).

Vavg=1/T integral Pi to 0 Vmsin wt dt (v average is equal to 1/t its cycle integral limits π to 0 t max or V Peek sin omega t derivate with respect to d).

= Vp/T ( -COSwt/w)limit T/2 to 0.

or simple is that Vavg=Vm/π.