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A 2 KVA, 200 / 2000 V single phase transformer is converted into 200 / 2200 V auto-transformer, then the KVA rating of the new transformer will be
- a)20 KVA
- b)44 KVA
- c)22 KVA
- d)24 KVA
Correct answer is option 'C'. Can you explain this answer?
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A 2 KVA, 200 / 2000 V single phase transformer is converted into 200 /...
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A 2 KVA, 200 / 2000 V single phase transformer is converted into 200 /...
Given:
- Original transformer: 2 KVA, 200 / 2000 V (single phase)
- Converted into an auto-transformer: 200 / 2200 V
To find:
- KVA rating of the new transformer
1. Determine the turns ratio:
- The original transformer has a turns ratio of 200/2000, which can be simplified to 1/10.
- The auto-transformer has a voltage ratio of 200/2200, which can be simplified to 1/11.
2. Calculate the transformation ratio:
- The transformation ratio is the ratio of the number of turns on the primary side to the number of turns on the secondary side.
- In the original transformer, the number of turns on the primary side is 1 and on the secondary side is 10, so the transformation ratio is 1:10.
- In the auto-transformer, the number of turns on the primary side is 1 and on the secondary side is 11, so the transformation ratio is 1:11.
3. Calculate the KVA rating:
- The KVA rating is proportional to the square of the turns ratio.
- In the original transformer, the turns ratio is 1:10, so the KVA rating is (1/10)^2 * 2 KVA = 0.2 KVA.
- In the auto-transformer, the turns ratio is 1:11, so the KVA rating is (1/11)^2 * X KVA, where X is the KVA rating of the new transformer.
4. Solve for X:
- To find the KVA rating of the new transformer, we can equate the KVA ratings of the original and auto-transformer.
- 0.2 KVA = (1/11)^2 * X KVA
- X = 0.2 KVA * (11/1)^2 = 0.2 KVA * 121 = 24.2 KVA
5. Final answer:
- The KVA rating of the new transformer is approximately 24.2 KVA, which can be rounded to 24 KVA.
- Therefore, the correct answer is option 'd', 24 KVA.
- Original transformer: 2 KVA, 200 / 2000 V (single phase)
- Converted into an auto-transformer: 200 / 2200 V
To find:
- KVA rating of the new transformer
Step-by-step solution:
1. Determine the turns ratio:
- The original transformer has a turns ratio of 200/2000, which can be simplified to 1/10.
- The auto-transformer has a voltage ratio of 200/2200, which can be simplified to 1/11.
2. Calculate the transformation ratio:
- The transformation ratio is the ratio of the number of turns on the primary side to the number of turns on the secondary side.
- In the original transformer, the number of turns on the primary side is 1 and on the secondary side is 10, so the transformation ratio is 1:10.
- In the auto-transformer, the number of turns on the primary side is 1 and on the secondary side is 11, so the transformation ratio is 1:11.
3. Calculate the KVA rating:
- The KVA rating is proportional to the square of the turns ratio.
- In the original transformer, the turns ratio is 1:10, so the KVA rating is (1/10)^2 * 2 KVA = 0.2 KVA.
- In the auto-transformer, the turns ratio is 1:11, so the KVA rating is (1/11)^2 * X KVA, where X is the KVA rating of the new transformer.
4. Solve for X:
- To find the KVA rating of the new transformer, we can equate the KVA ratings of the original and auto-transformer.
- 0.2 KVA = (1/11)^2 * X KVA
- X = 0.2 KVA * (11/1)^2 = 0.2 KVA * 121 = 24.2 KVA
5. Final answer:
- The KVA rating of the new transformer is approximately 24.2 KVA, which can be rounded to 24 KVA.
- Therefore, the correct answer is option 'd', 24 KVA.
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