Problem $7.(15$ points$)$ You are designing a power supply for a $100$ W high$-$quality audio amplifier that will drive an $8$ Ohm speaker load. The datasheet says you need approximately a $75$ V Vcc rail to properly supply the transistor power stage. To get the excellent performance you expect, you aim for $1\%$ ripple, and choose a design that minimizes the amount of capacitance required to reduce cost. Assume the diode drop is $0\mathrm{.}7$ V$,$ and the input AC voltage available from a transformer is $75$ sin$(377$t$)$ V$.$a$)$ How much capacitance do you need for a maximum load current $($a real$-$world value in uF$)?$b$)$ What is the ripple voltage at$10$ W output power?c$)$ What should be the minimum voltage rating of the capacitor$($s$)?$