Q$3.$ Transformers connected in open$-$delta supply four $50$kW$,3-$phase, $400$V induction motors from an $11$kV line. At full load, each motor has an efficiency of $95\%$ and operates at $0\mathrm{.}80$p$.$f lagging.

a$)$ Determine kVA rating of each of the two transformers and their turns ratio.

b$)$ Determine the line currents on HV and LV sides. At what power factor is each transformer operating?

c$)$ What is the real power supplied by each transformer?

d$)$ What would be the available capacity, if a third transformer of same rating is used to form the closed delta?