A synchronous motor can operate at

lagging power factor only
leading power factor only
unity power factor only
lagging, leading and unity power factors

The correct answer is D. lagging, leading and unity power factors.

A synchronous motor is an AC electric motor that rotates at a constant speed regardless of the load on the motor. The speed of a synchronous motor is determined by the frequency of the AC power supply and the number of poles on the motor.

Synchronous motors can operate at lagging, leading, and unity power factors. The power factor of a 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). A lagging power factor means that the current is lagging behind the voltage, while a leading power factor means that the current is leading the voltage. A unity power factor means that the current is in phase with the voltage.

The power factor of a synchronous motor can be controlled by changing the field current. When the field current is increased, the motor will operate at a lagging power factor. When the field current is decreased, the motor will operate at a leading power factor. When the field current is set to the value that causes the motor to operate at unity power factor, the motor is said to be operating at synchronous speed.

Synchronous motors are often used in applications where it is important to maintain a constant speed, such as in electric power generation and in variable-speed drives.