flem $2$: $(10$ Points$)$

The single$-$phase full$-$wave ac$-$controller in Fig. $2$ supplies an RL$-$load. The input rms voltage is $230-V,60$ Hz $.$ The load such that $L=26\mathrm{.}525mH$&$R=10-.$ If the load is consumed $50\%$ of the rated power, calculate:

$($a$)$ The conduction angle $$ and firing angles $.$

$($b$)$ Calculate the rms output voltage.

$($c$)$ The input power factors.

$(3$ points$)$

$($d$)$ Draw the load voltage and find the average voltage across T$2.$

$(1$ point$)$

$(1$ point$)$

$($e$)$ Find the rating of T $1$ and T $2($PIV$,$ average current. rms current and peak current$).$

$(2$ points$)$

$(3$ points$)$