Answer :
To solve this problem, we need to understand the relationship between the number of poles (P), the frequency (f), and the speed (N) of an alternator or motor.
The formula that relates these quantities for synchronous machines is:
[tex]N = \frac{120 \times f}{P}[/tex]
where:
- [tex]N[/tex] is the speed in revolutions per minute (RPM),
- [tex]f[/tex] is the frequency in hertz (Hz),
- [tex]P[/tex] is the number of poles.
Step-by-step Solution:
Determine the Speed of the Alternator:
- Given: The alternator has 10 poles and operates at 25 Hz.
- Using the formula for the alternator:
[tex]N_1 = \frac{120 \times 25}{10} = 300 \text{ RPM}[/tex] - So, the alternator runs at 300 revolutions per minute.
Matching the Motor Speed to the Alternator:
- The synchronous motor is directly coupled to the alternator, meaning the motor's speed is also 300 RPM.
Calculate the Number of Poles in the Motor:
- Given: The motor operates at 60 Hz.
- Using the formula for the motor:
[tex]300 = \frac{120 \times 60}{P_2}[/tex] - Solve for [tex]P_2[/tex]:
[tex]P_2 = \frac{120 \times 60}{300} = 24[/tex]
Therefore, the synchronous motor has 24 poles.
