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The transformation ratio of an auto transformer for a 30 kW, 400, 3-ϕ induction motor is______. If the starting torque is to be 75% of full load torque. Assume the full load slip to the 5% and the short circuit current to be 6 times the full load current.
- a)0.55
- b)0.75
Correct answer is between '0.55,0.75'. Can you explain this answer?
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The transformation ratio of an auto transformer for a 30 kW, 400, 3-ϕ...
As we know,
x2 = 0.41667
x = 0.645
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The transformation ratio of an auto transformer for a 30 kW, 400, 3-ϕ...
In an auto transformer, a portion of the winding is common to both the primary and secondary side. The transformation ratio of an auto transformer is given by the ratio of the number of turns on the secondary side to the number of turns on the primary side.
Given data:
- Motor power, P = 30 kW
- Line voltage, V = 400 V
- Slip at full load, S = 5%
- Starting torque = 0.75 * Full load torque
- Short circuit current = 6 * Full load current
To find the transformation ratio, we need to calculate the full load current and the full load torque.
1. Full Load Current (I):
The power (P) can be calculated using the formula:
P = √3 * V * I * Power factor
Rearranging the formula, we get:
I = P / (√3 * V * Power factor)
Assuming the power factor to be 0.8 (typical value for induction motors), we can calculate the full load current:
I = 30,000 / (√3 * 400 * 0.8) = 27.39 A
2. Full Load Torque (TFL):
The torque (T) can be calculated using the formula:
T = (P * 1000) / (2 * π * n)
Where n is the synchronous speed of the motor. For a 3-phase induction motor, the synchronous speed is given by:
n = (120 * Frequency) / Number of poles
Assuming a standard 4-pole motor and a frequency of 50 Hz, we can calculate the synchronous speed:
n = (120 * 50) / 4 = 1500 rpm
Substituting the values into the torque formula, we get:
TFL = (30,000 * 1000) / (2 * π * 1500) = 318.31 Nm
3. Starting Torque (TS):
The starting torque is given as 75% of the full load torque:
TS = 0.75 * TFL = 0.75 * 318.31 = 238.73 Nm
4. Transformation Ratio (TR):
The starting torque is directly proportional to the square of the transformation ratio. Therefore, we can calculate the transformation ratio using the formula:
TR = √(TS / TFL)
TR = √(238.73 / 318.31) ≈ 0.73
Since the short circuit current is not used in the calculation of the transformation ratio, it does not affect the answer. The correct answer lies between 0.55 and 0.75, and the calculated transformation ratio of 0.73 falls within this range. Therefore, the correct answer is option b) 0.75.
Given data:
- Motor power, P = 30 kW
- Line voltage, V = 400 V
- Slip at full load, S = 5%
- Starting torque = 0.75 * Full load torque
- Short circuit current = 6 * Full load current
To find the transformation ratio, we need to calculate the full load current and the full load torque.
1. Full Load Current (I):
The power (P) can be calculated using the formula:
P = √3 * V * I * Power factor
Rearranging the formula, we get:
I = P / (√3 * V * Power factor)
Assuming the power factor to be 0.8 (typical value for induction motors), we can calculate the full load current:
I = 30,000 / (√3 * 400 * 0.8) = 27.39 A
2. Full Load Torque (TFL):
The torque (T) can be calculated using the formula:
T = (P * 1000) / (2 * π * n)
Where n is the synchronous speed of the motor. For a 3-phase induction motor, the synchronous speed is given by:
n = (120 * Frequency) / Number of poles
Assuming a standard 4-pole motor and a frequency of 50 Hz, we can calculate the synchronous speed:
n = (120 * 50) / 4 = 1500 rpm
Substituting the values into the torque formula, we get:
TFL = (30,000 * 1000) / (2 * π * 1500) = 318.31 Nm
3. Starting Torque (TS):
The starting torque is given as 75% of the full load torque:
TS = 0.75 * TFL = 0.75 * 318.31 = 238.73 Nm
4. Transformation Ratio (TR):
The starting torque is directly proportional to the square of the transformation ratio. Therefore, we can calculate the transformation ratio using the formula:
TR = √(TS / TFL)
TR = √(238.73 / 318.31) ≈ 0.73
Since the short circuit current is not used in the calculation of the transformation ratio, it does not affect the answer. The correct answer lies between 0.55 and 0.75, and the calculated transformation ratio of 0.73 falls within this range. Therefore, the correct answer is option b) 0.75.
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The transformation ratio of an auto transformer for a 30 kW, 400, 3-ϕ induction motor is______. If the starting torque is to be 75% of full load torque. Assume the full load slip to the 5% and the short circuit current to be 6 times the full load current.a)0.55b)0.75Correct answer is between '0.55,0.75'. Can you explain this answer?
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The transformation ratio of an auto transformer for a 30 kW, 400, 3-ϕ induction motor is______. If the starting torque is to be 75% of full load torque. Assume the full load slip to the 5% and the short circuit current to be 6 times the full load current.a)0.55b)0.75Correct answer is between '0.55,0.75'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The transformation ratio of an auto transformer for a 30 kW, 400, 3-ϕ induction motor is______. If the starting torque is to be 75% of full load torque. Assume the full load slip to the 5% and the short circuit current to be 6 times the full load current.a)0.55b)0.75Correct answer is between '0.55,0.75'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The transformation ratio of an auto transformer for a 30 kW, 400, 3-ϕ induction motor is______. If the starting torque is to be 75% of full load torque. Assume the full load slip to the 5% and the short circuit current to be 6 times the full load current.a)0.55b)0.75Correct answer is between '0.55,0.75'. Can you explain this answer?.
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