The correct answer is: C. the rotor excitation and supply voltage both.
The maximum power developed in a synchronous motor will depend on the rotor excitation and supply voltage both. The rotor excitation is the current that flows through the rotor windings, and the supply voltage is the voltage that is applied to the stator windings. The maximum power developed in a synchronous motor occurs when the rotor excitation and supply voltage are in phase with each other.
Option A is incorrect because the maximum power developed in a synchronous motor will not depend on the rotor excitation only. The supply voltage must also be considered.
Option B is incorrect because the maximum power developed in a synchronous motor will not depend on the supply voltage only. The rotor excitation must also be considered.
Option D is incorrect because the maximum power developed in a synchronous motor will not depend on the rotor excitation, supply voltage, and maximum value of coupling angle (90°). The maximum power developed in a synchronous motor occurs when the rotor excitation and supply voltage are in phase with each other. The maximum value of coupling angle (90°) is not a factor in determining the maximum power developed in a synchronous motor.