Problem $3$: Given a balanced, $3$ phase, $\backslash (\backslash$Delta $\backslash )-\backslash ($ Y $\backslash )$ connected system with a line voltage at the source of $80\backslash ($ V$\_\{$R M S$\}\backslash ),$ a line impedance of $\backslash (4\backslash$Omega $\backslash ),$ and a load impedance per phase of $\backslash (24+$j $6\backslash$Omega $\backslash ).$

a$.$ Draw the single$-$phase equivalent circuit. Label all given voltages and impedances.

b$.$ Determine the magnitude of the line current.

c$.$ Determine the magnitude of the phase current at the load.

d$.$ Determine the magnitude of the line voltage at the load.

e$.$ Determine the magnitude of the phase voltage at the source.

f$.$ Determine the power factor at the source. $($include leading or lagging$)$

g$.$ Determine the total real power delivered to the $3-$phase load.