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The power input to a 415 V, 50 Hz, 6 pole 3- phase induction motor running at 975 rpm is 40kW. The stator losses are 1 kW and friction and windage losses total 2 kW. What is the efficiency of motor
- a)92.5%
- b)92%
- c)90%
- d)88%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The power input to a 415 V, 50 Hz, 6 pole 3- phase induction motor run...
power i/p = 40 kw
Slip = 0.025
Rotor i/p = 40 – 1 = 39 kw
GMPO = (1 - S) 39 = 38.025 kw
Shaft o/p = 38.025 – 2
= 36.025 kw
∴ η = 36.025/40 = 90%
Most Upvoted Answer
The power input to a 415 V, 50 Hz, 6 pole 3- phase induction motor run...
Given data:
Voltage (V) = 415 V
Frequency (f) = 50 Hz
Number of poles (p) = 6
Speed (N) = 975 rpm
Input power (P) = 40 kW
Stator losses (Ps) = 1 kW
Friction and windage losses (Pf) = 2 kW
Calculations:
1. Synchronous speed (Ns) = (120 * f) / p
= (120 * 50) / 6
= 1000 rpm
2. Slip (s) = (Ns - N) / Ns
= (1000 - 975) / 1000
= 0.025
3. Output power (Pout) = P - Ps - Pf
= 40 - 1 - 2
= 37 kW
4. Input current (I) = P / (sqrt(3) * V * power factor)
Assuming power factor (pf) = 0.85
I = 40 / (sqrt(3) * 415 * 0.85)
= 59.7 A
5. Power factor (pf) = Pout / (sqrt(3) * V * I)
= 37 / (sqrt(3) * 415 * 59.7)
= 0.79
6. Efficiency (η) = Pout / P
= 37 / 40
= 0.925 or 92.5%
Therefore, the efficiency of the motor is 92%. Option (c) is the correct answer.
Voltage (V) = 415 V
Frequency (f) = 50 Hz
Number of poles (p) = 6
Speed (N) = 975 rpm
Input power (P) = 40 kW
Stator losses (Ps) = 1 kW
Friction and windage losses (Pf) = 2 kW
Calculations:
1. Synchronous speed (Ns) = (120 * f) / p
= (120 * 50) / 6
= 1000 rpm
2. Slip (s) = (Ns - N) / Ns
= (1000 - 975) / 1000
= 0.025
3. Output power (Pout) = P - Ps - Pf
= 40 - 1 - 2
= 37 kW
4. Input current (I) = P / (sqrt(3) * V * power factor)
Assuming power factor (pf) = 0.85
I = 40 / (sqrt(3) * 415 * 0.85)
= 59.7 A
5. Power factor (pf) = Pout / (sqrt(3) * V * I)
= 37 / (sqrt(3) * 415 * 59.7)
= 0.79
6. Efficiency (η) = Pout / P
= 37 / 40
= 0.925 or 92.5%
Therefore, the efficiency of the motor is 92%. Option (c) is the correct answer.
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The power input to a 415 V, 50 Hz, 6 pole 3- phase induction motor run...
4. The power input to a 500-V, 50-Hz, 6-pole, 3-phase induction motor
running at 975 rpm is 40 kW. The stator losses are 1 kW and the friction
and windage losses total 2 kW. Calculate (a) the slip (b) the rotor copper
loss (C) shaft output (d) the efficiency.
Ans. [(a) 0.025 (b) 975 W (c) 36.1 kW (d) 90%)
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