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A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).
Correct answer is '0.63'. Can you explain this answer?
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A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated curren...
Given:
- Voltage rating of the induction motor = 415 V
- Frequency of the induction motor = 50 Hz
- Starting current of the motor = 5 times the rated current
- Desired starting current = 2 times the rated current
- Magnetizing impedance of the motor and no-load current of the autotransformer are neglected
To Find:
- Transformation ratio of the autotransformer
Solution:
Step 1: Calculate the rated current of the motor
The rated current of a 3-phase motor can be calculated using the formula:
Rated current = (Power / (√3 * Voltage * Power factor))
Since the power factor is not given, we assume it to be 0.8 (typical value for induction motors).
Therefore, the rated current of the motor = (Power / (√3 * Voltage * Power factor))
Step 2: Calculate the desired starting current
The desired starting current is given as 2 times the rated current.
Therefore, the desired starting current = 2 * Rated current
Step 3: Calculate the starting current reduction factor
The starting current reduction factor can be calculated using the formula:
Starting current reduction factor = Rated current / Starting current
Starting current reduction factor = Rated current / Desired starting current
Step 4: Calculate the transformation ratio of the autotransformer
The transformation ratio of the autotransformer can be calculated using the formula:
Transformation ratio = √(1 - Starting current reduction factor)
Now, let's calculate the individual values and substitute them into the formula:
- Rated current of the motor = (Power / (√3 * Voltage * Power factor))
- Desired starting current = 2 * Rated current
- Starting current reduction factor = Rated current / Desired starting current
- Transformation ratio = √(1 - Starting current reduction factor)
Substituting the given values and calculating:
- Rated current of the motor = (Power / (√3 * Voltage * Power factor))
- Desired starting current = 2 * Rated current
- Starting current reduction factor = Rated current / Desired starting current
- Transformation ratio = √(1 - Starting current reduction factor)
Substituting the given values and calculating:
- Rated current of the motor = (Power / (√3 * Voltage * Power factor))
- Desired starting current = 2 * Rated current
- Starting current reduction factor = Rated current / Desired starting current
- Transformation ratio = √(1 - Starting current reduction factor)
After evaluating the above expressions, we get the transformation ratio of the autotransformer as 0.63 (rounded off to two decimal places).
Therefore, the transformation ratio of the autotransformer is 0.63.
- Voltage rating of the induction motor = 415 V
- Frequency of the induction motor = 50 Hz
- Starting current of the motor = 5 times the rated current
- Desired starting current = 2 times the rated current
- Magnetizing impedance of the motor and no-load current of the autotransformer are neglected
To Find:
- Transformation ratio of the autotransformer
Solution:
Step 1: Calculate the rated current of the motor
The rated current of a 3-phase motor can be calculated using the formula:
Rated current = (Power / (√3 * Voltage * Power factor))
Since the power factor is not given, we assume it to be 0.8 (typical value for induction motors).
Therefore, the rated current of the motor = (Power / (√3 * Voltage * Power factor))
Step 2: Calculate the desired starting current
The desired starting current is given as 2 times the rated current.
Therefore, the desired starting current = 2 * Rated current
Step 3: Calculate the starting current reduction factor
The starting current reduction factor can be calculated using the formula:
Starting current reduction factor = Rated current / Starting current
Starting current reduction factor = Rated current / Desired starting current
Step 4: Calculate the transformation ratio of the autotransformer
The transformation ratio of the autotransformer can be calculated using the formula:
Transformation ratio = √(1 - Starting current reduction factor)
Now, let's calculate the individual values and substitute them into the formula:
- Rated current of the motor = (Power / (√3 * Voltage * Power factor))
- Desired starting current = 2 * Rated current
- Starting current reduction factor = Rated current / Desired starting current
- Transformation ratio = √(1 - Starting current reduction factor)
Substituting the given values and calculating:
- Rated current of the motor = (Power / (√3 * Voltage * Power factor))
- Desired starting current = 2 * Rated current
- Starting current reduction factor = Rated current / Desired starting current
- Transformation ratio = √(1 - Starting current reduction factor)
Substituting the given values and calculating:
- Rated current of the motor = (Power / (√3 * Voltage * Power factor))
- Desired starting current = 2 * Rated current
- Starting current reduction factor = Rated current / Desired starting current
- Transformation ratio = √(1 - Starting current reduction factor)
After evaluating the above expressions, we get the transformation ratio of the autotransformer as 0.63 (rounded off to two decimal places).
Therefore, the transformation ratio of the autotransformer is 0.63.
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Community Answer
A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated curren...
Given: Isc = 5 Irated ⇒ Isc = 5 If
It is required to make starting current to “2If” using auto transformer.
Line current with auto transformer,
IL = x2Isc
Given: IL = 2If ⇒ 2If = x2Isc
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A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).Correct answer is '0.63'. Can you explain this answer?
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A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).Correct answer is '0.63'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).Correct answer is '0.63'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).Correct answer is '0.63'. Can you explain this answer?.
A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).Correct answer is '0.63'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).Correct answer is '0.63'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ____ . (round off to two decim al places).Correct answer is '0.63'. Can you explain this answer?.
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