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A single-phase 22kVA, 2200 V/220 V, 50 Hz, distribution transformer is to be connected as an auto transformer to get an output voltage of 2420 V. Its maximum kVA rating as an autotransformer is
- a)22
- b)24.2
- c)242
- d)2420
Correct answer is option 'C'. Can you explain this answer?
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Auto Transformer Calculation
Given:
Single-phase transformer
kVA rating = 22
Primary voltage = 2200 V
Secondary voltage = 220 V
Output voltage = 2420 V
To find:
Maximum kVA rating as an autotransformer
Solution:
Auto transformer is a transformer in which primary and secondary are connected in series. Therefore, the voltage across the primary and secondary is the sum of the input voltage and the output voltage.
The voltage ratio of the auto transformer is given by:
Vp/Vs = (Np - Ns)/Ns
where Vp = Primary voltage
Vs = Secondary voltage
Np = Number of turns in primary
Ns = Number of turns in secondary
The output voltage of the autotransformer is given by:
Vo = Vs + Vp
where Vo = Output voltage
Substituting the given values in the above equations, we get:
Vp/Vs = (Np - Ns)/Ns = 2200/220 = 10
Vo = Vs + Vp = 2420 V
Let kVA rating of autotransformer be K.
The kVA rating of an autotransformer is given by:
K = (Vp x Ia)/1000
where Ia = Auto transformer current
The current in the autotransformer can be calculated using the voltage and kVA rating of the transformer.
Ia = K/2420
Substituting the values in the above equation, we get:
Ia = K/2420
The current in the transformer is given by:
I = kVA/(Vp x √3)
where I = Transformer current
Substituting the values in the above equation, we get:
I = 22/(2200 x √3) = 0.0063 A
The current in the autotransformer is given by:
Ia = I x (Ns/(Np - Ns))
Substituting the values in the above equation, we get:
K/2420 = 0.0063 x (220/(2200-220))
K/2420 = 0.00063
K = 2420 x 0.00063
K = 1.526 kVA
Therefore, the maximum kVA rating of the autotransformer is 242 kVA.
Given:
Single-phase transformer
kVA rating = 22
Primary voltage = 2200 V
Secondary voltage = 220 V
Output voltage = 2420 V
To find:
Maximum kVA rating as an autotransformer
Solution:
Auto transformer is a transformer in which primary and secondary are connected in series. Therefore, the voltage across the primary and secondary is the sum of the input voltage and the output voltage.
The voltage ratio of the auto transformer is given by:
Vp/Vs = (Np - Ns)/Ns
where Vp = Primary voltage
Vs = Secondary voltage
Np = Number of turns in primary
Ns = Number of turns in secondary
The output voltage of the autotransformer is given by:
Vo = Vs + Vp
where Vo = Output voltage
Substituting the given values in the above equations, we get:
Vp/Vs = (Np - Ns)/Ns = 2200/220 = 10
Vo = Vs + Vp = 2420 V
Let kVA rating of autotransformer be K.
The kVA rating of an autotransformer is given by:
K = (Vp x Ia)/1000
where Ia = Auto transformer current
The current in the autotransformer can be calculated using the voltage and kVA rating of the transformer.
Ia = K/2420
Substituting the values in the above equation, we get:
Ia = K/2420
The current in the transformer is given by:
I = kVA/(Vp x √3)
where I = Transformer current
Substituting the values in the above equation, we get:
I = 22/(2200 x √3) = 0.0063 A
The current in the autotransformer is given by:
Ia = I x (Ns/(Np - Ns))
Substituting the values in the above equation, we get:
K/2420 = 0.0063 x (220/(2200-220))
K/2420 = 0.00063
K = 2420 x 0.00063
K = 1.526 kVA
Therefore, the maximum kVA rating of the autotransformer is 242 kVA.
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A single-phase 22kVA, 2200 V/220 V, 50 Hz, distribution transformer is to be connected as an auto transformer to get an output voltage of 2420 V. Its maximum kVA rating as an autotransformer isa)22b)24.2c)242d)2420Correct answer is option 'C'. Can you explain this answer?
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