A generator with V g $=300$ V and Zg $=50$ is connected to a load ZL $=75$ through a $50$ lossless line of length l $=0\mathrm{.}15$$.($a$)$ Compute Zin, the input impedance of the line at the generator end. $($b$)$ Compute $$Ii and V i$.($c$)$ Compute the time$-$average power delivered to the line, Pin $=12$Re$[$V i $$I $$ i $].($d$)$ Compute V L$,$IL$,$ and the time$-$average power delivered to the load, PL $=12$Re$[$V L $$I $$ L $].$ How does Pin compare to PL$?$ Explain. $($e$)$ Compute the time$-$average power delivered by the generator, Pg$,$ and the time$-$average power dissipated in Zg$.$ Is conservation of power satisfied?