b$)$ A $20-$pole, $415$V $50$HZ $3-,$ Y connected synchronous motor is operating at no$-$load with normal excitation. It has armature resistance per phase of zero and synchronous reactance of $8.$ If rotor is $0\mathrm{.}5($mechanical$)$ from its synchronous position. Calculate;

i$)$ Rotor displacement in degrees

ii$)$ Armature emf $/$phase

iii$)$ Armature current$/$phase

iv$)$ Power drawn by the motor

v$)$ Power developed by armature

Howwill these quantities changewhenmotor is loaded and the rotor displacementincreases to