Question

A 1,1kV, 60Hz, three-phase induction motor runs ar 1200r/min. Calculate the number of poles if the motor is operating
operating at a slip of 33%.

Answer 1

To calculate the number of poles of the motor, we can use the following formulas:

1. **Synchronous Speed (Ns)** can be calculated using the formula:
\[
Ns = \frac{120 \times f}{P}
\]
where:
- \(Ns\) = synchronous speed in revolutions per minute (rpm)
- \(f\) = frequency in hertz (Hz)
- \(P\) = number of poles

2. **Actual Speed (N)** and **Slip (S)** relationship:
\[
S = \frac{Ns - N}{Ns}
\]
Rearranging this, we get:
\[
Ns = \frac{N}{1 - S}
\]

Given:
- The motor runs at \(N = 1200 \, \text{rpm}\)
- The slip \(S = 33\% = 0.33\)

Now we can calculate the synchronous speed \(Ns\):
\[
Ns = \frac{1200}{1 - 0.33} = \frac{1200}{0.67} \approx 1790.15 \, \text{rpm}
\]

Now that we have \(Ns\), we can substitute it into the first synchronous speed formula to find the number of poles \(P\):
\[
1790.15 = \frac{120 \times 60}{P}
\]

Now, rearranging for \(P\):
\[
P = \frac{120 \times 60}{1790.15} \approx \frac{7200}{1790.15} \approx 4.02
\]

Since the number of poles must be a whole number, we round to the nearest whole number, which gives \(P = 4\).

Thus, the number of poles in the motor is **4 poles**.