Problem $3$: Given a balanced, $3$ phase, $\backslash (\backslash$Delta$-\backslash$mathrm$\{$Y$\}\backslash )$ connected system with a line voltage at the load of $\backslash (100\backslash$mathrm$\{$~V$\}\_\{\backslash$mathrm$\{$RMS$\}\}\backslash ),$ a line impedance of $\backslash (8\backslash$Omega $\backslash ),$ and a load impedance per phase of $\backslash (20-\backslash$mathrm$\{$j$\}15\backslash$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 source.

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.