$[$Q$7]$ Self commutation circuit of thyristor connected to a $220$ V source and energizing a heater of $15$ Ohms. The heating cycle varies between $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to $\backslash (90^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ where the temperature rises with $\backslash (2\backslash$mathrm$\{$uS$\}/\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The maximum SCR current must not exceed $4$ times the average value.

$1-$Determine the values of inductance and capacitance the realizing the mentioned temperature range

$2-$Select the elements using appropriate datasheet

$3-$Plot the performances Vc$,$ Io$,$ IL$,$ Vo$,...$