The correct answer is B. increases with increase in its excitation.
A synchronous machine is a rotating machine that converts electrical energy into mechanical energy or vice versa. It is a three-phase machine with a stator and a rotor. The stator is the stationary part of the machine, and the rotor is the rotating part. The stator is wound with three-phase windings, and the rotor is wound with a single-phase winding.
The excitation of a synchronous machine is the amount of current that flows through the rotor winding. The excitation current determines the magnetic field of the machine. The magnetic field of the machine interacts with the stator windings to produce an electric current.
The stability of a synchronous machine is its ability to maintain its speed and output power under load changes. The stability of a synchronous machine is affected by its excitation. When the excitation of a synchronous machine is increased, the magnetic field of the machine is increased. This increases the torque that the machine produces, and the machine becomes more stable.
When the excitation of a synchronous machine is decreased, the magnetic field of the machine is decreased. This decreases the torque that the machine produces, and the machine becomes less stable.
Therefore, the stability of a synchronous machine increases with increase in its excitation.