Question III.6: (a) How does a dc motor work? Explain the functions of brush...
(a) How does a dc motor work? Explain the functions of brushes and commutators by providing the constructional details of a dc motor.
(b) A six pole, three-phase synchronous generator driven at 1000 rpm supplies power to an induction motor running at 1440 rpm on full load. Calculate the percentage slip of the motor and the number of poles of the motor.
(a) Refer to Sections 7.1-7.2.2 on Pages 7.1-7.8.
(b) The synchronous generator is rotated at a synchronous speed of 1000 rpm by a prime mover. The synchronous speed N_{s} is expressed as
N_{s}=\frac{120 f}{P} where f is the frequency of the generated EMF
\begin{aligned} \text {or,} \quad f &=\frac{N_{s} \times P}{120} \\&=\frac{1000 \times 6}{120}=50 Hz\end{aligned}This synchronous generator now supplies power to the induction motor at a frequency of 50 Hz. The synchronous speed of the rotating magnetic field produced in the motor is
and N_{s}=\frac{120 \times f}{P}=\frac{120 \times 50}{2}=3000 rpm (for P = 2)
N_{s}=\frac{120 \times 50}{4}=1500 rpm (for P = 4)
The motor speed is 1440 rpm, which should be slightly less than the synchronous speed. Logically, the number of poles of the motor must be 4.
Percentage slip, S=\frac{N_{s}-N_{r}}{N_{s}} \times 100=\frac{(1500-1440) \times 100}{1500}=4 per cent.