The correct answer is: D. none of the above.
The power factor of a synchronous motor is unity when the inductive reactance of the motor is equal to the resistance of the motor. This occurs when the armature current is at a certain value, but it is not necessarily the maximum or minimum value.
The armature current is the current that flows through the armature winding of the motor. The inductive reactance of the motor is the opposition to the flow of current caused by the inductance of the motor windings. The resistance of the motor is the opposition to the flow of current caused by the resistance of the motor windings.
When the inductive reactance of the motor is equal to the resistance of the motor, the current that flows through the armature windings is in phase with the voltage applied to the motor. This means that the power factor of the motor is unity.
The power factor of a motor is a measure of how efficiently the motor converts electrical energy into mechanical energy. A power factor of unity indicates that the motor is converting all of the electrical energy into mechanical energy. A power factor of less than unity indicates that the motor is not converting all of the electrical energy into mechanical energy. The energy that is not converted into mechanical energy is lost as heat.
The power factor of a motor can be improved by using a power factor correction capacitor. A power factor correction capacitor is a capacitor that is connected to the motor in parallel. The capacitor helps to reduce the inductive reactance of the motor. This reduces the current that flows through the armature windings and improves the power factor of the motor.