Question $1.$ Transmission efficiency $(25$ points$)$

Figure $1.$ Per$-$phase transmission efficiency diagram for question $1.$

a$.$ Consider the simplified per$-$phase power transmission diagram of Figure $1,$ with an ideal transformer placed near the load impedance. The load voltage is a constant $\backslash (\backslash$left$|\backslash$hat$\{$V$\}\_\{$L$\}\backslash$right$|=480$ V$\_\{$R M S$\}\backslash )$ and $120$MW of $3-$phase load power is being transmitted $100$ km over $00$AWG $(9\mathrm{.}2565$ mm diameter$)$ solid aluminum conductors. For this analysis, assume the transmission line is purely resistive.

i$.(10$ pts$)$ Calculate the total AC transmission resistance of the $100$ km long wire, assuming room temperature $(300$K$).$

ii$.$ What $(8$ pts$)$ transmission phase voltage magnitude $\backslash (\backslash$left$|\backslash$hat$\{$V$\}\_\{\backslash$text $\{$trans $\}\}\backslash$right$|\backslash )($in RMS volts$)$ and transformer $(7$ pts$)$ turns ratio $\text{'}$a$\text{'}$ is required to achieve a minimum transmission efficiency of $\backslash (90\backslash \%\backslash )$ at this power level?