Final answer:
The speed of the 4-pole, 3-phase alternator is 1500 rpm. The open-circuit phase voltage is approximately 19.84 kV, and the line voltage is approximately 34.36 kV.
Step-by-step explanation:
The problem at hand involves calculating the speed and open-circuit line and phase voltages of a 4-pole, 3-phase, 50 Hz, star-connected alternator with 36 slots and 30 conductors per slot, given a flux per pole of 0.0496 Wb with a sinusoidal distribution. Let's break down the problem into two parts: calculating the speed of the alternator and then calculating the line and phase voltages.
Calculating Speed
The speed of the alternator can be calculated using the formula:
Speed (n) = (120 × frequency) / number of poles
For our case:
Speed (n) = (120 × 50 Hz) / 4 = 1500 rpm
Calculating Voltage
The phase voltage (Ep) of an alternator can be found using the formula:
Ep = 4.44 × f × ϕ × T
Where f is the frequency, ϕ is the flux per pole, and T is the total number of turns per phase. To find T, we can multiply the number of slots per pole per phase by the number of conductors per slot, and then by the number of phases present (since it's a star connection, the same number of turns per phase is assumed).
Slots per pole per phase = Total slots / (number of poles × number of phases)
= 36 / (4 × 3) = 3
Total turns per phase (T) = Slots per pole per phase × conductors per slot
= 3 × 30 = 90 turns
Now, we calculate the phase voltage (Ep):
Ep = 4.44 × 50 Hz × 0.0496 Wb × 90 turns
= 19.84 kV approximately
To find the line voltage (Vl), we use the relationship between line and phase voltages in a star connection:
Vl = √3 × Ep
Vl = √3 × 19.84 kV = 34.36 kV approximately