$8\mathrm{.}7$ A single$-$phase full$-$wave diode rectifier is supplied from a $\backslash (60-\backslash$mathrm$\{$Hz$\}\backslash )$ source. The average and peak DC$-$bus voltages of the rectifier are $148$ V and $155\mathrm{.}56$ V $,$ respectively, when $\backslash (75\backslash$Omega $\backslash )$ load is connected. Calculate:

$($a$)$ The peak and RMS values of the source voltage.

$($b$)$ The ripple in the output voltage and value of the DC$-$bus capacitance.

$($c$)$ The peak current of the diode.

$($d$)$ The ripple in the output voltage if load resistance becomes $\backslash (40\backslash$Omega $\backslash ).$