Maximum Speed Calculation of 3 Phase Squirrel Cage Induction Motor

The maximum possible speed of a 3 phase squirrel cage induction motor can be calculated using the formula:

\[
N_{max} = \frac{120 \times f}{P}
\]

where:
- \( N_{max} \) = maximum speed of the motor (rpm)
- \( f \) = frequency of the power supply (Hz)
- \( P \) = number of poles in the motor

Given Data:
- Slip (\( S \)) = 4%
- Number of poles (\( P \)) = ? (not provided)

To calculate the maximum speed of the motor, we need to know the number of poles in the motor. The slip can be used to determine the number of poles using the formula:

\[
S = \frac{Ns - Nr}{Ns} \times 100
\]

where:
- \( Ns \) = synchronous speed of the motor (rpm)
- \( Nr \) = rotor speed of the motor (rpm)

Calculation:
Given that the slip (\( S \)) is 4%, we can assume that the rotor speed (\( Nr \)) is 96% of the synchronous speed (\( Ns \)).

Therefore, \( Nr = 0.96 \times Ns \)

Substitute the values in the formula:

\[
4 = \frac{Ns - 0.96 \times Ns}{Ns} \times 100
\]

Solving the above equation, we get \( Ns = 1500 \) rpm

Now, substitute the values of \( f \) and \( P \) in the formula for maximum speed:

\[
N_{max} = \frac{120 \times 50}{P} = \frac{6000}{P}
\]

Therefore, the maximum possible speed of the 3 phase squirrel cage induction motor running at a slip of 4% is 6000/P rpm, where \( P \) is the number of poles in the motor.