Singly-excited and doubly-excited magnetic systems are two types of electromechanical systems that utilize the interaction between magnetic fields and electric currents. These systems have different applications and characteristics, and the correct answer is option 'A', which states that singly-excited magnetic systems correspond to reluctance motors, while doubly-excited magnetic systems correspond to synchronous motors.

Singly-Excited Magnetic Systems:
- Reluctance Motors: These motors operate based on the principle of magnetic reluctance, which is the opposition offered by a magnetic circuit to the magnetic flux. In reluctance motors, a single excitation source, typically a direct current (DC) source, is used to create a magnetic field. The stator and rotor of the motor have salient poles with teeth, which create a variation in the magnetic reluctance as they rotate. This variation in reluctance causes the rotor to align with the stator poles and produce rotational motion. Reluctance motors are commonly used in applications where precise speed control is not required, such as in fans, blowers, and pumps.

Doubly-Excited Magnetic Systems:
- Synchronous Motors: These motors rely on the interaction between two magnetic fields - the stator field and the rotor field. The stator field is generated by the stator windings, which are typically supplied with three-phase alternating current (AC). The rotor field is created by direct current (DC) supplied to the rotor windings through slip rings and brushes. The rotor field rotates at the same speed as the stator field, resulting in synchronous motion. Synchronous motors are known for their ability to maintain constant speed under varying loads, making them suitable for applications requiring precise speed control, such as in industrial machinery, compressors, and generators.

In summary, singly-excited magnetic systems, such as reluctance motors, use a single excitation source to create a magnetic field, while doubly-excited magnetic systems, such as synchronous motors, utilize two magnetic fields - the stator field and the rotor field - to produce synchronous motion.