The correct answer is: C. The back e.m.f. decreases causing an increase in motor current.
When a load is applied to a synchronous motor, the rotor has to turn faster in order to keep up with the rotating field. This causes the back e.m.f. to decrease, which in turn causes the motor current to increase.
The back e.m.f. is an induced voltage that opposes the current flow in the armature windings. It is proportional to the speed of the rotor. When the load is applied, the rotor slows down, which causes the back e.m.f. to decrease. This decrease in back e.m.f. causes the current to increase, which in turn causes the motor to speed up. This process continues until the rotor is turning at the same speed as the rotating field.
The options A, B, and D are incorrect.
Option A is incorrect because the increased load does not have to take more current. The current drawn by the load is determined by the power required by the load.
Option B is incorrect because the rotor does not shift its phase backward. The rotor always stays in step with the rotating field.
Option D is incorrect because the rotor does not strengthen the rotating field. The rotating field is created by the stator windings.