If the field of a synchronous motor is underexcited, the power factor will be

zero
unity
lagging
leading

The correct answer is C. lagging.

When the field of a synchronous motor is underexcited, the magnetic field produced by the stator windings is stronger than the magnetic field produced by the rotor windings. This causes the rotor to lag behind the stator field, which results in a lagging power factor.

Option A is incorrect because the power factor cannot be zero. The power factor is a measure of how efficiently the electrical energy is being used. A power factor of zero would mean that no electrical energy is being used, which is not possible.

Option B is incorrect because the power factor is not always unity. The power factor is only unity when the electrical load is purely resistive. When the electrical load is inductive or capacitive, the power factor will be less than unity.

Option D is incorrect because the power factor is not always leading. The power factor is only leading when the electrical load is capacitive. When the electrical load is inductive or resistive, the power factor will be lagging.