Question

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

(b) A 72 KVA transformer supplies

(i) a heating and lighting load of 12 KW at unity power factor

(ii) a motor load of 70 kVA at 0.766 (lagging) power factor.

Calculate the minimum rating of the power-factor improvement capacitors which must be connected in the circuit the ensure that the transformer does not become overloaded. (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: