The stator of a 3-phase induction motor has 4 slots per pole phase. If the supply frequency is 50 Hz, calculate the number of stator poles produced and the total number of slots on the stator, respectively.
8 poles and 96 slots
The question asks us to determine the number of stator poles produced and the total number of slots on the stator of a 3-phase induction motor, given the number of slots per pole phase and the supply frequency.
We are given:
- Number of slots per pole per phase = 4
- Number of phases = 3 (since it's a 3-phase motor)
- Supply frequency = 50 Hz
The total number of slots on the stator is related to the number of slots per pole per phase, the number of poles, and the number of phases by the following formula:
Total number of stator slots = (Number of slots per pole per phase) $\times$ (Number of poles) $\times$ (Number of phases)
Let $N_{slots}$ be the total number of stator slots and $P$ be the number of poles.
Using the given values:
\( N_{slots} = 4 \times P \times 3 \)
\( N_{slots} = 12P \)
Calculating Stator Poles and Total Slots
This equation tells us that the total number of slots must be 12 times the number of poles. We can now look at the options provided to see which pair of (Poles, Total slots) satisfies this relationship.
| Option | Number of Poles (P) | Total Slots (Nslots) | Check \(12P = N_{slots}\) | Match? |
|---|---|---|---|---|
| 1 | 8 | 96 | \(12 \times 8 = 96\) | Yes |
| 2 | 8 | 54 | \(12 \times 8 = 96\) | No (96 \(\neq\) 54) |
| 3 | 6 | 54 | \(12 \times 6 = 72\) | No (72 \(\neq\) 54) |
| 4 | 6 | 96 | \(12 \times 6 = 72\) | No (72 \(\neq\) 96) |
From the table, only Option 1 provides a pair of poles and total slots that satisfies the relationship \( N_{slots} = 12P \) derived from the given slots per pole phase and number of phases.
Therefore, the number of stator poles produced is 8, and the total number of slots on the stator is 96.
The supply frequency of 50 Hz is relevant for determining the synchronous speed (\(N_s = \frac{120f}{P}\)), but it is not needed for calculating the number of poles or total slots based on the slots per pole phase information provided in this question.
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