A single$-$phase full$-$wave ac controller shown in Fig. P$3\mathrm{.}1$ is used to control the power from a $2300-V$ ac source into an R$-$L load circuit with $R=2\mathrm{.}30$ and $x_L=L=2\mathrm{.}30($inductive reactance$).$

$($a$)$ Determine the control range $($that is$,$ the range of variation of the delay angle $$ necessary to very the current from zero to maximum possible value$).$

$($b$)$ Determine the maximum RMS line current.

$($c$)$ The maximum power.

$($d$)$ The delay angle $=\frac{}{2}.$

$($i$)$ Determine the RMS thyristor current.

$($ii$)$ Determine conduction angle.

$($iii$)$Determine the power factor at source.

$($e$)$ Carefully sketch and label $($with values$)$ the waveforms for $v_0,v_{T1},$ and $v_{T2}$ on the same graph. Label the sketches and show SCRs conduction pattern.

$($f$)$ Carefully sketch and label $($with values$)$ the waveforms for $i_0,i_{T1},$ and $i_{T2}$ on the same graph. Label the sketches and show SCRs conduction pattern.