$4\mathrm{.}75$ Augment the rectifier circuit of Problem $4\mathrm{.}68$ with a capacitor chosen to provide a peak$-$to$-$peak ripple voltage of $($i$)10\%$ of the peak output and $($ii$)1\%$ of the peak output. In each case:

$($a$)$ What average output voltage results?

$($b$)$ What fraction of the cycle does the diode conduct?

$($c$)$ What is the average diode current?

$($d$)$ What is the peak diode current?