A buck$$boost regulator has an input voltage Vs $=12$ V$.$ The duty cycle k $=0\mathrm{.}6,$ and the switching frequency is $25$ kHz$.$ If L $=200$ H$,$ C $=250$ F$,$ and the average load current is Ia $=1\mathrm{.}2$ A$,$ determine $($a$)$ the average output voltage Va$,($b$)$ the peak$-$to$-$peak output ripple voltage $$Vc$,($c$)$ the peak to$-$peak ripple current of inductor $$I$,$ and $($d$)$ the critical values of L and C