You have been tasked with designing a power distribution system. The power is generated by a $600$ kW generator that is $100$ km from the destination site. The generator outputs a single phase $120$ V rms $60$ Hz AC voltage. The transmission wire has a resistance of $\backslash (10^\{-4\}\backslash$Omega $/\backslash$mathrm$\{$m$\}\backslash ).$ The destination site requires at least $500$ kW of power available at $\backslash (120\backslash$mathrm$\{$~V$\}\backslash$mathrm$\{$rms$\},60\backslash$mathrm$\{$~Hz$\}\backslash ).$

Assume that the load$/$destination utilizes as much power as possible.

As one part of the load, design a full wave rectifier circuit to produce a DC signal of $12$ V with less than $\backslash (5\backslash \%\backslash )$ variation at the destination site for a $\backslash (10\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash )$ load. To simplify the math, you let $\backslash ($ V$\_\{$F$\}\backslash )$ to be $1$ V $.$ Clearly state all your assumptions in your analysis.

a$)$ Write the stages that go into this system.

b$)$ Why is it desirable to have extremely high voltages through transmission lines $($as opposed to running $120/240$V through the lines$)?$

c$)$ Design and draw the system