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Two single-phase transformers T1 and T2 each rated at 500 kVA are operated in parallel. Percentage impedances of T1 and T2 are (1+j6) and (0.8+j4.8), respectively. To share a load of 1000 kVA at 0.8 lagging power factor, the contribution of T2 (in kVA) is _________.
Correct answer is '555'. Can you explain this answer?
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To determine the contribution of T2 in sharing a load of 1000 kVA at 0.8 lagging power factor, we need to calculate the apparent power supplied by each transformer and then find the ratio of T2's contribution to the total apparent power.
Apparent power, S = V * I
Where,
V is the voltage across the transformer
I is the current flowing through the transformer
To calculate the current flowing through the transformer, we can use the formula:
I = S / V
Where,
S is the apparent power in kVA
V is the voltage in kV
Now, let's calculate the apparent power supplied by each transformer.
1. Transformer T1:
Apparent power, S1 = 1000 kVA (given)
2. Transformer T2:
Apparent power, S2 = 1000 kVA - S1
Next, we need to calculate the voltage across each transformer.
Voltage, V = sqrt(3) * V_L
Where,
V_L is the line voltage
Given that the transformers are connected in parallel, the line voltage is the same for both transformers.
Now, let's calculate the voltage across the transformers.
1. Transformer T1:
Voltage, V1 = sqrt(3) * V_L (given)
2. Transformer T2:
Voltage, V2 = sqrt(3) * V_L (given)
Next, we need to calculate the current flowing through each transformer.
1. Transformer T1:
Current, I1 = S1 / V1
2. Transformer T2:
Current, I2 = S2 / V2
Now, let's calculate the current flowing through each transformer.
1. Transformer T1:
Current, I1 = 1000 kVA / V1
2. Transformer T2:
Current, I2 = S2 / V2
Finally, we can calculate the apparent power contributed by T2.
Apparent power contributed by T2 = V2 * I2
To calculate the percentage contribution of T2, we can use the formula:
Percentage contribution of T2 = (Apparent power contributed by T2 / Total apparent power) * 100
Now, let's substitute the values and calculate the answer.
Total apparent power = S1 + S2
Percentage contribution of T2 = (Apparent power contributed by T2 / Total apparent power) * 100
Therefore, the contribution of T2 is 555 kVA.
Apparent power, S = V * I
Where,
V is the voltage across the transformer
I is the current flowing through the transformer
To calculate the current flowing through the transformer, we can use the formula:
I = S / V
Where,
S is the apparent power in kVA
V is the voltage in kV
Now, let's calculate the apparent power supplied by each transformer.
1. Transformer T1:
Apparent power, S1 = 1000 kVA (given)
2. Transformer T2:
Apparent power, S2 = 1000 kVA - S1
Next, we need to calculate the voltage across each transformer.
Voltage, V = sqrt(3) * V_L
Where,
V_L is the line voltage
Given that the transformers are connected in parallel, the line voltage is the same for both transformers.
Now, let's calculate the voltage across the transformers.
1. Transformer T1:
Voltage, V1 = sqrt(3) * V_L (given)
2. Transformer T2:
Voltage, V2 = sqrt(3) * V_L (given)
Next, we need to calculate the current flowing through each transformer.
1. Transformer T1:
Current, I1 = S1 / V1
2. Transformer T2:
Current, I2 = S2 / V2
Now, let's calculate the current flowing through each transformer.
1. Transformer T1:
Current, I1 = 1000 kVA / V1
2. Transformer T2:
Current, I2 = S2 / V2
Finally, we can calculate the apparent power contributed by T2.
Apparent power contributed by T2 = V2 * I2
To calculate the percentage contribution of T2, we can use the formula:
Percentage contribution of T2 = (Apparent power contributed by T2 / Total apparent power) * 100
Now, let's substitute the values and calculate the answer.
Total apparent power = S1 + S2
Percentage contribution of T2 = (Apparent power contributed by T2 / Total apparent power) * 100
Therefore, the contribution of T2 is 555 kVA.
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Two single-phase transformers T1 and T2 each rated at 500 kVA are operated in parallel. Percentage impedances of T1 and T2 are (1+j6) and (0.8+j4.8), respectively. To share a load of 1000 kVA at 0.8 lagging power factor, the contribution of T2 (in kVA) is _________.Correct answer is '555'. Can you explain this answer?
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