$2.(5$ points each$)$ Answer the following questions about the rectifier and Zener shunt regulator circuit boln$$m

b$.$ The Zener shunt regulator will operate properly as long as the Zener diode is conducting at least $50$ mA in reverse breakdown. Find the minimum voltage $\backslash (\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$A$\}\}\backslash )$ to ensure that the regulator continues to function with the attached load.

c$.$ Suppose the rectifier DC output voltage is the same as the peak $\backslash ($ A C $\backslash )$ voltage into the rectifier. Will this circuit work from a $\backslash (120$ V$\_\{\backslash$text $\{$rms $\}\}$ A C $\backslash )$ supply? Explain.

d$.$ Find the capacitor size required to ensure that the rectifier voltage ripple is $0\mathrm{.}55$ V $.$ You can assume that the capacitor discharges for half an AC cycle, or $8\mathrm{.}3$ ms $.$