Problem $3[25$ points$]$:

Consider the three$-$phase balanced circuit shown below $($left$)$:

Assume: $V_a=\frac{{120}^V}{{?}_0},Z_Y=\frac{3^{32}}{{?}_{20}},Z_{Ln}=\frac{1^{12}}{{?}_{80}}$

$($a$)-$ Find the source Line$-$to$-$Line voltage $(V_{ab}).$

$b(k^{\text{'}})-$ Find the line current $(I_a).$

$($c$)-$ Find the load phase voltage $(V_{AN}).$

$($d$)-$ Find the $3-$phase complex, apparent, real, and reactive powers for the source.

$($e$)-$ Find the power factor of the source.