Question:
A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is _________.
A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is _________.
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To find the rotor speed of an induction motor, use the formula \( N_r = N_s \times (1 - \text{Slip}) \), where \( N_s \) is the synchronous speed and \( \text{Slip} \) is the slip at full load.
Updated On: Nov 25, 2025
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Correct Answer: 1440
Solution and Explanation
We are given the following values:
- Voltage = 440 V
- Power = 8 kW
- Number of poles = 4
- Frequency = 50 Hz
- Slip = 0.04
Step 1: Calculate synchronous speed (\( N_s \))
The synchronous speed \( N_s \) is the speed at which the magnetic field rotates and is given by the formula: \[ N_s = \frac{120 \times \text{Frequency}}{\text{Number of Poles}}. \] Substituting the given values: \[ N_s = \frac{120 \times 50}{4} = 1500 \, \text{rpm}. \] Step 2: Calculate the rotor speed (\( N_r \))
The rotor speed at full load can be calculated using the slip formula: \[ N_r = N_s (1 - \text{Slip}). \] Substituting the values: \[ N_r = 1500 \times (1 - 0.04) = 1500 \times 0.96 = 1440.0 \, \text{rpm}. \] Thus, the rotor speed at full load is \( 1440.0 \, \text{rpm} \).
- Power = 8 kW
- Number of poles = 4
- Frequency = 50 Hz
- Slip = 0.04
Step 1: Calculate synchronous speed (\( N_s \))
The synchronous speed \( N_s \) is the speed at which the magnetic field rotates and is given by the formula: \[ N_s = \frac{120 \times \text{Frequency}}{\text{Number of Poles}}. \] Substituting the given values: \[ N_s = \frac{120 \times 50}{4} = 1500 \, \text{rpm}. \] Step 2: Calculate the rotor speed (\( N_r \))
The rotor speed at full load can be calculated using the slip formula: \[ N_r = N_s (1 - \text{Slip}). \] Substituting the values: \[ N_r = 1500 \times (1 - 0.04) = 1500 \times 0.96 = 1440.0 \, \text{rpm}. \] Thus, the rotor speed at full load is \( 1440.0 \, \text{rpm} \).
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