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For a single phase, two winding transformer, the supply frequency and voltage are both increased by 10%. The percentage changes in the hysteresis loss and eddy current loss, respectively, are
- a)10 and 21
- b)-10 and 21
- c)21 and 10
- d)-21 and 10
Correct answer is option 'A'. Can you explain this answer?
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For a single phase, two winding transformer, the supply frequency and ...
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For a single phase, two winding transformer, the supply frequency and ...
Solution:
Given, a single-phase, two-winding transformer, the supply frequency and voltage are increased by 10%.
Let's understand the hysteresis and eddy current losses in a transformer.
Hysteresis Loss:
- It is the energy loss occurring in the transformer core due to the reversal of magnetization.
- It depends on the magnetic properties of the core material and the maximum flux density.
- It is proportional to the frequency and the square of the maximum flux density.
Eddy Current Loss:
- It is the energy loss occurring in the transformer core due to the circulating currents induced in the core.
- It depends on the resistivity of the core material, the thickness of the laminations, and the frequency.
- It is proportional to the square of the frequency and the square of the thickness of the laminations.
Now, let's calculate the percentage changes in hysteresis and eddy current losses.
Percentage change in Hysteresis Loss:
- As the supply frequency and voltage are increased by 10%, the maximum flux density also increases by 10%.
- Therefore, the hysteresis loss will increase by 10% (proportional to the square of the maximum flux density).
- Hence, the percentage change in hysteresis loss is 10%.
Percentage change in Eddy Current Loss:
- As the supply frequency is increased by 10%, the eddy current loss will increase by 21% (proportional to the square of the frequency).
- However, as the supply voltage is also increased by 10%, the thickness of the laminations will decrease by approximately 5% (proportional to the square root of the voltage).
- Therefore, the eddy current loss will decrease by approximately 5% (proportional to the square of the thickness of the laminations).
- Hence, the percentage change in eddy current loss is 21% - 5% = 16%.
Therefore, the correct option is (a) 10% and 16%.
Given, a single-phase, two-winding transformer, the supply frequency and voltage are increased by 10%.
Let's understand the hysteresis and eddy current losses in a transformer.
Hysteresis Loss:
- It is the energy loss occurring in the transformer core due to the reversal of magnetization.
- It depends on the magnetic properties of the core material and the maximum flux density.
- It is proportional to the frequency and the square of the maximum flux density.
Eddy Current Loss:
- It is the energy loss occurring in the transformer core due to the circulating currents induced in the core.
- It depends on the resistivity of the core material, the thickness of the laminations, and the frequency.
- It is proportional to the square of the frequency and the square of the thickness of the laminations.
Now, let's calculate the percentage changes in hysteresis and eddy current losses.
Percentage change in Hysteresis Loss:
- As the supply frequency and voltage are increased by 10%, the maximum flux density also increases by 10%.
- Therefore, the hysteresis loss will increase by 10% (proportional to the square of the maximum flux density).
- Hence, the percentage change in hysteresis loss is 10%.
Percentage change in Eddy Current Loss:
- As the supply frequency is increased by 10%, the eddy current loss will increase by 21% (proportional to the square of the frequency).
- However, as the supply voltage is also increased by 10%, the thickness of the laminations will decrease by approximately 5% (proportional to the square root of the voltage).
- Therefore, the eddy current loss will decrease by approximately 5% (proportional to the square of the thickness of the laminations).
- Hence, the percentage change in eddy current loss is 21% - 5% = 16%.
Therefore, the correct option is (a) 10% and 16%.
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For a single phase, two winding transformer, the supply frequency and voltage are both increased by 10%. The percentage changes in the hysteresis loss and eddy current loss, respectively, area)10 and 21b)-10 and 21c)21 and 10d)-21 and 10Correct answer is option 'A'. Can you explain this answer?
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