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A 2000/1000/500 three winding transformer is to be used as auto transformer with supply of 3000 V. Two loads of 1050 kVA at 3500V,and other one at 180 kVA at 1000V. The total kVA supplied will be
- a)1230 kVA
- b)1440 kVA
- c)1680 kVA
- d)1150 kVA
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A 2000/1000/500 three winding transformer is to be used as auto transf...
Total kVA = 1050+180 = 1230 kVA.
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A 2000/1000/500 three winding transformer is to be used as auto transf...
Calculating the Total kVA Supplied in an Auto Transformer
Given Data:
- Primary winding: 2000/1000/500 V
- Supply voltage: 3000 V
- Load 1: 1050 kVA at 3500 V
- Load 2: 180 kVA at 1000 V
Step 1: Determine the Turns Ratio
To use the transformer as an auto-transformer, we need to determine the turns ratio between the primary and secondary windings. The turns ratio can be calculated as follows:
Turns ratio = Primary voltage / Secondary voltage
For the given transformer, the primary voltage is 2000/1000/500 V, and the secondary voltage is 3000 V. Therefore, the turns ratio is:
Turns ratio = (2000/1000/500) / 3000 = 2/3
Step 2: Calculate the Load Voltage
Since the transformer is being used as an auto-transformer, the load voltage will be different from the secondary winding voltage. We can calculate the load voltage using the turns ratio:
Load voltage = Turns ratio * Secondary voltage
For Load 1, the secondary voltage is 3500 V. Therefore, the load voltage is:
Load voltage = (2/3) * 3500 = 2333.33 V
For Load 2, the secondary voltage is 1000 V. Therefore, the load voltage is:
Load voltage = (2/3) * 1000 = 666.67 V
Step 3: Calculate the Load kVA
The load kVA can be calculated using the load voltage and load power (kW) for each load.
For Load 1, the load power is 1050 kVA. Therefore, the load kVA is:
Load kVA 1 = 1050 kVA
For Load 2, the load power is 180 kVA. Therefore, the load kVA is:
Load kVA 2 = 180 kVA
Step 4: Calculate the Total kVA Supplied
Finally, we can calculate the total kVA supplied by adding the load kVA for each load:
Total kVA supplied = Load kVA 1 + Load kVA 2
Total kVA supplied = 1050 kVA + 180 kVA = 1230 kVA
Therefore, the correct answer is option 'A', 1230 kVA.
Given Data:
- Primary winding: 2000/1000/500 V
- Supply voltage: 3000 V
- Load 1: 1050 kVA at 3500 V
- Load 2: 180 kVA at 1000 V
Step 1: Determine the Turns Ratio
To use the transformer as an auto-transformer, we need to determine the turns ratio between the primary and secondary windings. The turns ratio can be calculated as follows:
Turns ratio = Primary voltage / Secondary voltage
For the given transformer, the primary voltage is 2000/1000/500 V, and the secondary voltage is 3000 V. Therefore, the turns ratio is:
Turns ratio = (2000/1000/500) / 3000 = 2/3
Step 2: Calculate the Load Voltage
Since the transformer is being used as an auto-transformer, the load voltage will be different from the secondary winding voltage. We can calculate the load voltage using the turns ratio:
Load voltage = Turns ratio * Secondary voltage
For Load 1, the secondary voltage is 3500 V. Therefore, the load voltage is:
Load voltage = (2/3) * 3500 = 2333.33 V
For Load 2, the secondary voltage is 1000 V. Therefore, the load voltage is:
Load voltage = (2/3) * 1000 = 666.67 V
Step 3: Calculate the Load kVA
The load kVA can be calculated using the load voltage and load power (kW) for each load.
For Load 1, the load power is 1050 kVA. Therefore, the load kVA is:
Load kVA 1 = 1050 kVA
For Load 2, the load power is 180 kVA. Therefore, the load kVA is:
Load kVA 2 = 180 kVA
Step 4: Calculate the Total kVA Supplied
Finally, we can calculate the total kVA supplied by adding the load kVA for each load:
Total kVA supplied = Load kVA 1 + Load kVA 2
Total kVA supplied = 1050 kVA + 180 kVA = 1230 kVA
Therefore, the correct answer is option 'A', 1230 kVA.
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Question Description
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