$(10$ Points in Total$)-$A three$-$phase synchronous generator produces an open$-$circuit line voltage of $6,928V$ when the dc exciting current is $50$ A $.$ The ac terminals are then short$-$circuited, and the three$-$line currents are found to be $800$A$.$

a$)$ Calculate the synchronous reactance per phase $(2$ points$).$

b$)$ Calculate the terminal voltage if three $12-$ resistors are connected in wye across the terminals $(4$ points$).$

c$)$ Sketch the phasor diagram for part b$)$ above $(4$ points$).$