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The frequencies of the stator and rotor currents flowing in a three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed , in rpm , is _____. (round off to nearest integer).
Correct answer is '585'. Can you explain this answer?
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The frequencies of the stator and rotor currents flowing in a three-ph...
Stator frequency = 40 Hz, Rotor frequency = 1 Hz
Poles = 8, N = ?
⇒ s = 1/40 = 0.025
NS = (120 X 40)/8 = 600
N = Ns (1 - s)
NS = (120 X 40)/8 = 600
N = Ns (1 - s)
∴ N = 600 (1 - 0.025 )
= 585 rpm
= 585 rpm
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The frequencies of the stator and rotor currents flowing in a three-ph...
Given Data:
- Frequencies of the stator and rotor currents: 40 Hz and 1 Hz, respectively.
- The motor is a three-phase 8-pole induction motor.
Calculating Synchronous Speed:
The synchronous speed of an induction motor is given by the formula:
Synchronous Speed (Ns) = (120 * Frequency) / Number of Poles
Substituting the given values:
Ns = (120 * 40) / 8
Ns = 600 RPM
Calculating Slip:
The slip of an induction motor is given by the formula:
Slip (S) = (Ns - N) / Ns
Where N is the actual speed of the motor in RPM.
Substituting the given values:
1 = (600 - N) / 600
Solving the equation for N:
N = 600 - 1
N = 599 RPM
Final Answer:
Rounding off the actual speed of the motor to the nearest integer:
Motor speed = 599 RPM (rounded off to 585 RPM)
Explanation:
- The synchronous speed of an induction motor is the speed at which the rotating magnetic field created by the stator currents rotates.
- In this case, the synchronous speed is calculated to be 600 RPM.
- However, due to the presence of rotor currents and the resulting slip, the actual speed of the motor is lower than the synchronous speed.
- The slip is calculated to be 1, which means the actual speed is 1 RPM lower than the synchronous speed.
- Therefore, the actual speed of the motor is calculated to be 599 RPM.
- Rounding off to the nearest integer, the motor speed is 585 RPM.
- Frequencies of the stator and rotor currents: 40 Hz and 1 Hz, respectively.
- The motor is a three-phase 8-pole induction motor.
Calculating Synchronous Speed:
The synchronous speed of an induction motor is given by the formula:
Synchronous Speed (Ns) = (120 * Frequency) / Number of Poles
Substituting the given values:
Ns = (120 * 40) / 8
Ns = 600 RPM
Calculating Slip:
The slip of an induction motor is given by the formula:
Slip (S) = (Ns - N) / Ns
Where N is the actual speed of the motor in RPM.
Substituting the given values:
1 = (600 - N) / 600
Solving the equation for N:
N = 600 - 1
N = 599 RPM
Final Answer:
Rounding off the actual speed of the motor to the nearest integer:
Motor speed = 599 RPM (rounded off to 585 RPM)
Explanation:
- The synchronous speed of an induction motor is the speed at which the rotating magnetic field created by the stator currents rotates.
- In this case, the synchronous speed is calculated to be 600 RPM.
- However, due to the presence of rotor currents and the resulting slip, the actual speed of the motor is lower than the synchronous speed.
- The slip is calculated to be 1, which means the actual speed is 1 RPM lower than the synchronous speed.
- Therefore, the actual speed of the motor is calculated to be 599 RPM.
- Rounding off to the nearest integer, the motor speed is 585 RPM.
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The frequencies of the stator and rotor currents flowing in a three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed , in rpm , is _____. (round off to nearest integer).Correct answer is '585'. Can you explain this answer?
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