A three-phase line, which has an impedance of \((2+j 4) \Omega\) per phase, feeds two balanced three-phase loads that are connected in parallel. One of the loads is Y-connected with an impedance of \((30+j 40) \Omega\) per phase, and the other is \(\Delta\)-connected with an impedance of \((60-j 45) \Omega\) per phase. The line is energized at the sending end from a \(60-\mathrm{Hz}\), threephase, balanced voltage source of \(120 \sqrt{3} \mathrm{~V}\) (rms, line-to-line). Determine

(a) the current, real power, and reactive power delivered by the sending-end source;

(b) the line-to-line voltage at the load;

(c) the current per phase in each load; and

(d) the total three-phase real and reactive powers absorbed by each load and by the line. Check that the total threephase complex power delivered by the source equals the total three-phase power absorbed by the line and loads.