A controlled half$-$wave rectifier has an R$-$L load as shown in Fig. P$1\mathrm{.}1.$ A freewheeling diode is placed in parallel with the load. The inductance is large enough to maintain ripple$-$free load current. The source is

$120$ V $($rms$)$ at $60$ Hz and the delay angle is $50.$

$($a$)$ The load resistance $R=20.$

$($i$)$ Determine the average load current.

$($ii$)$ Determine the rms load current.

$($b$)($i$)$ Determine the power absorbed by the resistor

$($ii$)$ Determine input power in volt$-$amperes.

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

$($c$)$ Carefully sketch and label $($with values$)$ the steady$-$state waveforms $v_L(t)$ and $v_{T1}(t)$ on the same graph.

$($d$)$ Carefully sketch and label $($with values$)$ the steady$-$state waveforms $i_{T1}(t)$ and $i_{D1}(t)$ on the same graph.