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The power input to a 3-phase, 50 Hz, 400 V, the 4-pole induction motor is 60 kW, and its stator losses are 1 kW. If this motor is running at 4% slip, the rotor copper loss is-
- a)1.18 kW
- b)2.36 kW
- c)0.18 kW
- d)0.36 kW
Correct answer is option 'B'. Can you explain this answer?
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Calculation of Rotor Copper Loss
Given parameters:
- Power input (Pin) = 60 kW
- Stator losses (Pst) = 1 kW
- Supply voltage (V) = 400 V
- Frequency (f) = 50 Hz
- Number of poles (p) = 4
- Slip (s) = 4%
Step 1: Calculate the stator input power (Pi)
Pi = Pin + Pst
Pi = 60 kW + 1 kW
Pi = 61 kW
Step 2: Calculate the synchronous speed (Ns)
Ns = (120 x f) / p
Ns = (120 x 50) / 4
Ns = 1500 rpm
Step 3: Calculate the rotor speed (Nr)
Nr = (1 - s) x Ns
Nr = (1 - 0.04) x 1500
Nr = 1440 rpm
Step 4: Calculate the rotor copper loss (Pc)
Pc = 3 x I^2 x Rr
where I = stator current and Rr = rotor resistance
To find I, we need to calculate the stator impedance (Zs) first.
Zs = V / I
Zs = 400 / I
The stator current (I) can be calculated using the stator input power (Pi) and the supply voltage (V).
Pi = 3 x V x I x cos(θ)
cos(θ) = 1 (assumed for simplicity)
I = Pi / (3 x V)
I = 61,000 / (3 x 400)
I = 152.5 A
Now we can calculate the rotor resistance (Rr) using the slip (s) and the rotor reactance (Xr).
Xr = Zs / s
Xr = (400 / 152.5) / 0.04
Xr = 6.58 Ω
Rr = Xr / (2 x π x Nr)
Rr = 6.58 / (2 x 3.14 x 1440)
Rr = 0.0012 Ω
Finally, we can calculate the rotor copper loss (Pc).
Pc = 3 x I^2 x Rr
Pc = 3 x 152.5^2 x 0.0012
Pc = 2.36 kW
Therefore, the rotor copper loss is 2.36 kW.
Given parameters:
- Power input (Pin) = 60 kW
- Stator losses (Pst) = 1 kW
- Supply voltage (V) = 400 V
- Frequency (f) = 50 Hz
- Number of poles (p) = 4
- Slip (s) = 4%
Step 1: Calculate the stator input power (Pi)
Pi = Pin + Pst
Pi = 60 kW + 1 kW
Pi = 61 kW
Step 2: Calculate the synchronous speed (Ns)
Ns = (120 x f) / p
Ns = (120 x 50) / 4
Ns = 1500 rpm
Step 3: Calculate the rotor speed (Nr)
Nr = (1 - s) x Ns
Nr = (1 - 0.04) x 1500
Nr = 1440 rpm
Step 4: Calculate the rotor copper loss (Pc)
Pc = 3 x I^2 x Rr
where I = stator current and Rr = rotor resistance
To find I, we need to calculate the stator impedance (Zs) first.
Zs = V / I
Zs = 400 / I
The stator current (I) can be calculated using the stator input power (Pi) and the supply voltage (V).
Pi = 3 x V x I x cos(θ)
cos(θ) = 1 (assumed for simplicity)
I = Pi / (3 x V)
I = 61,000 / (3 x 400)
I = 152.5 A
Now we can calculate the rotor resistance (Rr) using the slip (s) and the rotor reactance (Xr).
Xr = Zs / s
Xr = (400 / 152.5) / 0.04
Xr = 6.58 Ω
Rr = Xr / (2 x π x Nr)
Rr = 6.58 / (2 x 3.14 x 1440)
Rr = 0.0012 Ω
Finally, we can calculate the rotor copper loss (Pc).
Pc = 3 x I^2 x Rr
Pc = 3 x 152.5^2 x 0.0012
Pc = 2.36 kW
Therefore, the rotor copper loss is 2.36 kW.
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The power input to a 3-phase, 50 Hz, 400 V, the 4-pole induction moto...
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The power input to a 3-phase, 50 Hz, 400 V, the 4-pole induction motor is 60 kW, and its stator losses are 1 kW. If this motor is running at 4% slip, the rotor copper loss is-a)1.18 kWb)2.36 kWc)0.18 kWd)0.36 kWCorrect answer is option 'B'. Can you explain this answer?
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The power input to a 3-phase, 50 Hz, 400 V, the 4-pole induction motor is 60 kW, and its stator losses are 1 kW. If this motor is running at 4% slip, the rotor copper loss is-a)1.18 kWb)2.36 kWc)0.18 kWd)0.36 kWCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The power input to a 3-phase, 50 Hz, 400 V, the 4-pole induction motor is 60 kW, and its stator losses are 1 kW. If this motor is running at 4% slip, the rotor copper loss is-a)1.18 kWb)2.36 kWc)0.18 kWd)0.36 kWCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The power input to a 3-phase, 50 Hz, 400 V, the 4-pole induction motor is 60 kW, and its stator losses are 1 kW. If this motor is running at 4% slip, the rotor copper loss is-a)1.18 kWb)2.36 kWc)0.18 kWd)0.36 kWCorrect answer is option 'B'. Can you explain this answer?.
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