A $2300-V,1000hp,0\mathrm{.}8-PF$ leading, $60-Hz,$ two$-$pole, Y$-$connected synchronous motor has a synchronous reactance of $2\mathrm{.}8$ ohms and an armature resistance of $0\mathrm{.}4$ ohms $.$ At $60$ Hz $,$ its friction and windage losses are $24$ kW $,$ and its core losses are $18$ kW $.$ The field circuit has a dc voltage of $200$ V $,$ and the maximum $I_F$ is $10$ A $.$ The open$-$circuit characteristic of this motor is shown in Figure below. Answer the following questions about the motor, assuming that it is being supplied by an infinite bus.

a$)$ How much field current would be required to make this machine operate at Unity power factor when supplying full load?

b$)$ What is the motor's efficiency at full load and unity power factor?

c$)$ If the field current were increased by $5$ percent, what would the new value of the armature current be$?$ What would the new power factor be$?$ How much reactive power is being consumed or supplied by the motor?

d$)$ What is the maximum torque this machine is theoretically capable of supplying at unity power factor? At $0\mathrm{.}8$ PF leading?