The single$-$phase half$-$wave controlled rectifier supplies a resistive load draws an average current of $1\mathrm{.}624.$ If the converter is operated from a $240$ V$,50$ Hz supply and if the average value of the output voltage is $81$V$,$ calculate the following:

$($a$)$ The firing angle $..$

$($b$)$ Load resistance.

$($c$)$ The rms load voltage.

$($d$)$ The rms load current.

$($e$)$ The output d$.$c$.$ power.

$($f$)$ The ripple factor.