$(15$ points$)$ A balanced wye$-$connected load with $\frac{?}{\text{b}\text{a}\text{r}}(Z{)}_Y=\frac{30}{{?}_{30}}$ per phase is supplied by a balanced three$-$phase wye$-$connected source $(120$ V line$-$to$-$neutral, $f=60Hz).$ Use $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_{AN}$ as the reference voltage, i$.$e$.,\frac{?}{\text{b}\text{a}\text{r}}(V{)}_{AN}=\frac{120}{{?}_0}V.$

a$)$ Compute the currents across the load, $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_{an}\frac{,}{b}ar(I{)}_{bn},$ and $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_{cn}$ and the supply power factor.

b$)$ Compute the transmission line currents, $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_{Aa}\frac{,}{b}ar(I{)}_{Bb},$ and $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_{Cc}.$

c$)$ If a delta$-$connected capacitor bank with impedance $-j180$ per phase is connected in parallel with the load, recompute the supply power factor and the transmission line currents.