Question

(a) What are the factors which determine the synchronous speed of a motor? (6)

(b) Three conductors fitted side by side in the stator of a salient-pole alternator. Each generates a maximum voltage of 200V (sinusoidal). The angle subtended at the centre of the stator between adjacent conductors is 20 electrical degrees. If the three conductors are connected in series, find:

(a) the r.m.s. value of the effective voltage and

(b) the 'breadth factor'. Using the theory that is the basis of this problem, give one reason why three-phase current has been introduced. (10)

Answer 1

Part (a)

The synchronous speed of an AC motor is determined by two primary factors:

Supply Frequency (f)
Number of Poles (P)

The relationship between these factors and the synchronous speed (Ns) is given by the formula:

$$N_{s}=\frac{120f}{P}$$

Where Ns is the synchronous speed in revolutions per minute (RPM), f is the supply frequency in hertz, and P is the number of poles.

For example,

A 2-pole motor (P=2) running on a 50 Hz supply (f=50) will have a synchronous speed of 3000 RPM.
A 4-pole motor (P=4) on the same supply will have a synchronous speed of 1500 RPM.

In practical applications, especially for induction motors, the actual operating speed is slightly less than the synchronous speed due to a phenomenon known as slip, which is necessary for torque production.

For synchronous motors, the rotor locks in step with the stator's rotating magnetic field, and thus operates precisely at the synchronous speed.

✓ Verified Model Answer (Text Solution)

The synchronous speed of an AC motor is determined by two primary factors: