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The maximum efficiency of a 100 kVA transformer having iron loss of 900 kW and full load Cu loss of 1600 W occurs at________kVA.
- a)56.3
- b)133.3
- c)75
- d)177.7
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The maximum efficiency of a 100 kVA transformer having iron loss of 90...
Maximum efficiency at = kVA X √( Wi / Wcu )
= kVA X √ ( 900 / 1600 ) = 75 % of full load.
Where Wi = iron loss, Wcu = copper loss.
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The maximum efficiency of a 100 kVA transformer having iron loss of 90...
Given data:
Transformer rating = 100 kVA
Iron loss = 900 kW
Full load Cu loss = 1600 W
To find: Maximum efficiency and corresponding kVA rating
Formula used:
Efficiency =Output power / (Output power + losses)
Output power = Input power - losses
Calculation:
Let’s assume the transformer’s full load kVA rating be x.
So, the input power will be equal to the output power.
Output power = Input power = x kVA
Total losses = Iron loss + Cu loss = 900000 W + 1600 W = 901600 W
Input power = Output power + losses
x = x + 901600
x = 901600 / 1000
x = 901.6 kVA
Efficiency = Output power / (Output power + losses)
Efficiency = x / (x + 901600)
Differentiating efficiency w.r.t kVA rating x and equating to zero for maximum efficiency
d( Efficiency ) / d( x ) = 0
- x / (x+901600)^2 + 901600 / (x+901600)^2 = 0
- x + 901600 = 0
x = 901.6 kVA
Therefore, the maximum efficiency of the transformer occurs at 75 kVA (nearest to 901.6 kVA) which is option (C).
Hence, Option (C) is the correct answer.
Transformer rating = 100 kVA
Iron loss = 900 kW
Full load Cu loss = 1600 W
To find: Maximum efficiency and corresponding kVA rating
Formula used:
Efficiency =Output power / (Output power + losses)
Output power = Input power - losses
Calculation:
Let’s assume the transformer’s full load kVA rating be x.
So, the input power will be equal to the output power.
Output power = Input power = x kVA
Total losses = Iron loss + Cu loss = 900000 W + 1600 W = 901600 W
Input power = Output power + losses
x = x + 901600
x = 901600 / 1000
x = 901.6 kVA
Efficiency = Output power / (Output power + losses)
Efficiency = x / (x + 901600)
Differentiating efficiency w.r.t kVA rating x and equating to zero for maximum efficiency
d( Efficiency ) / d( x ) = 0
- x / (x+901600)^2 + 901600 / (x+901600)^2 = 0
- x + 901600 = 0
x = 901.6 kVA
Therefore, the maximum efficiency of the transformer occurs at 75 kVA (nearest to 901.6 kVA) which is option (C).
Hence, Option (C) is the correct answer.
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