When the field of a synchronous motor is under-excited, the power factor will be

The correct answer is B. lagging.

When the field of a synchronous motor is under-excited, the current drawn by the motor is leading the voltage. This is because the motor is acting as a capacitor, and capacitors draw leading current.

The other options are incorrect because:

• Option A is incorrect because the power factor will be lagging, not leading.
• Option C is incorrect because the power factor will not be unity.
• Option D is incorrect because the power factor will not be zero.

I hope this helps! Let me know if you have any other questions.