A single$-$phase voltage controller has the following data:

Source voltage $=230$V at $50$Hz$,$ Load $=0+$ j$4$Omega $.$ Calculate $($i$)$ the control range of firing angle, $($ii$)$ the maximum value of rms load current, $($iii$)$ the maximum value of average and rms thyristor currents, $($iv$)$ the maximum value of di$/$dt that may occur in the thyristors, $($v$)$ the value of conduction angle for alpha $=90$ deg assuming gate pulse width of radians.