Figure P8-77. shows a three-phase power system that is used in a manufacturing plant. The three sources are shown in the phasor diagram, with \(V_{\mathrm{P}}\) given as \(339.5 \mathrm{~V}\). The system is driving three balanced inductive loads of \(Z_{Y}=25^{+} j 1.88 \Omega\) each. The system frequency is \(60 \mathrm{~Hz}\).

(a) Build the circuit in Multisim and calculate the four currents \(\mathbf{I}_{\mathrm{A}}, \mathbf{I}_{\mathrm{B}}, \mathbf{I}_{\mathrm{C}}\), and \(\mathbf{I}_{\mathrm{N}}\). Ground the circuit at node \(\mathrm{N}\). To measure \(\mathbf{I}_{\mathrm{N}}\), insert a tiny resistor of \(1 \mu \Omega\) at point X. Plot the resulting currents (except \(\mathbf{I}_{\mathrm{N}}\) ) on the phasor diagram.

(b) Find the line-to-line voltages, that is \(\mathbf{V}_{\mathrm{AB}}, \mathbf{V}_{\mathrm{BC}}\), and \(\mathbf{V}\) \(\mathrm{CA}_{\mathrm{A}}\), and plot those on a phasor diagram. How are they related to the three source voltages?

(c) To save money, the plant manager posits that since there is almost no current flowing in \(\mathbf{I}_{\mathrm{N}}\) that it need not be wired. Comment on the manager's idea.