For the rectifier circuit above, $\backslash ($ v$\_\{$i n$\}\backslash )$ is a sinusoidal source with an amplitude of $127$ V and a frequency of $\backslash (\backslash$mathbf$\{10$ H z$\}\backslash ).$ NOTE the change in frequency, it is not $60$ Hz $.$ The transformer is an ideal $10$:$1$ step down transformer. The diode is on when it has a forward voltage drop of $0\mathrm{.}7$ V across it$.$

a$)$ If the capacitor is not present, what are the maximum and minimum voltages at the output, $\backslash ($ v$\_\{\backslash$text $\{$out $\}\}\backslash ).$

b$)$ Choose a capacitance value such that the voltage at the output drops by $\backslash (5\backslash \%\backslash )$ of the peak output voltage over the period of the input signal.