The correct answer is: D. over-excited
A synchronous motor can be used as a synchronous capacitor when it is over-excited. This is because when a synchronous motor is over-excited, the current it draws from the power supply is leading the voltage. This means that the motor is acting as a source of reactive power, which is the same as a capacitor.
When a synchronous motor is under-loaded or over-loaded, it will still draw current from the power supply, but the current will be lagging the voltage. This means that the motor is acting as a load, and it will consume real power from the power supply.
When a synchronous motor is under-excited, the current it draws from the power supply will be leading the voltage, but the current will be less than when the motor is over-excited. This means that the motor will still act as a source of reactive power, but it will be a smaller source than when it is over-excited.
In summary, a synchronous motor can be used as a synchronous capacitor when it is over-excited. This is because when a synchronous motor is over-excited, the current it draws from the power supply is leading the voltage. This means that the motor is acting as a source of reactive power, which is the same as a capacitor.