The correct answer is: C. leading power factor with under-excitation.
A synchronous motor is a type of electric motor that has a rotating magnetic field that is synchronized with the stator windings. The stator windings are connected to an external power source, and the rotating magnetic field is created by the current flowing through the stator windings. The rotor of the synchronous motor is made of a permanent magnet or a field winding that is excited by a DC current.
The power factor of a synchronous motor is the ratio of the real power (the power that is used to do work) to the apparent power (the product of the voltage and current). The power factor of a synchronous motor is affected by the excitation of the motor. When the motor is under-excited, the power factor is leading. This means that the current leads the voltage. When the motor is over-excited, the power factor is lagging. This means that the current lags the voltage.
In the question, the synchronous motor is connected to infinite bus-bars and has at constant full load, 100% excitation and unity power factor. This means that the motor is operating at its rated power and the power factor is unity. If the excitation is changed, the power factor will change. If the excitation is decreased, the power factor will become leading. This is because the current will lead the voltage when the motor is under-excited. If the excitation is increased, the power factor will become lagging. This is because the current will lag the voltage when the motor is over-excited.
Therefore, the correct answer is: C. leading power factor with under-excitation.