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A one-phase, 50 Hz, 40 kVA transformer with a ratio of 2000 V/250 V has a primary resistance of 1.15 Ω and a secondary resistance of 0.0155 Ω. Calculate total copper loss on half of the full load.
- a)856.8 W
- b)214.2 W
- c)642.6 W
- d)428.4 W
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A one-phase, 50 Hz, 40 kVA transformer with a ratio of 2000 V/250 V ha...
Concept:
Consider a two winding single phase transformer as shown below,
N1 = primary winding turns
N2 = secondary winding turns
V1 = primary winding voltage
V2 = secondary winding voltage
I1 = current through the primary winding
I2 = current through the secondary winding
Transformation ratio: It is defined as the ratio of the secondary voltage to the primary voltage. It is denoted by K.
Transformer equivalent circuit with respect to secondary can be represented a show below
Where R02 = Effective resistance of the transformer as referred to the secondary side of the transformer.
R02 = R2 + R1' ------- (2)
R1' = Equivalent primary resistance as referred to the secondary winding
R1' = R1 × K 2 ------ (3)
Similarly, effective resistance of the transformer as referred to the primary side of the transformer is given as,
R01 = R1 + R2'
R2' = Equivalent secondary resistance as referred to the primary winding
R2' = R2 / K 2
Calculation:
Given data
V1 = 2000 V, V2 = 250 V, R1 = 1.15 Ω, R2 = 0.0155 Ω
From equation(1)
K= V2 / V1
K = 250 / 2000
K = 1 / 8
Effective resistance of the transformer as referred to the secondary of the transformer.
From equations(2) & (3)
R02 = 0.0155 + 1.15 / 82
R02 = 0.0335 Ω
Power output P = 40 kVA
V2 I2 = 40 × 103
I2 = 40000 / 250
I2 = 160 A = Ifl
Ifl is the full load current flowing through the secondary.
We required to find power loss at half full load condition
So, current at half full load is given as,
∴ Total power loss at half full load condition is given as,
Phfl = I2hfl × R02
Phfl = 802 × 0.0335
Phfl = 214.2 W
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Community Answer
A one-phase, 50 Hz, 40 kVA transformer with a ratio of 2000 V/250 V ha...
Calculation of Total Copper Loss on Half of Full Load:
Given Data:
- Power rating of the transformer (S) = 40 kVA
- Voltage ratio (V1/V2) = 2000 V/250 V
- Primary resistance (R1) = 1.15 Ω
- Secondary resistance (R2) = 0.0155 Ω
Formula for Copper Loss:
- Copper loss = I^2 * R
Calculations:
1. Calculate the full load current (I2):
- S = V2 * I2
- 40 kVA = 250 V * I2
- I2 = 40,000 VA / 250 V = 160 A
2. Calculate the current on half of full load:
- I_half = I2 / 2 = 160 A / 2 = 80 A
3. Calculate the voltage on primary side (V1):
- V1 = V2 * (V1/V2) = 250 V * (2000/250) = 2000 V
4. Calculate the current on primary side (I1):
- I1 = S / V1 = 40,000 VA / 2000 V = 20 A
5. Calculate the total resistance (R_total) on primary side:
- R_total = R1 + (V1/V2)^2 * R2
- R_total = 1.15 Ω + (2000/250)^2 * 0.0155 Ω
- R_total = 1.15 Ω + 400 * 0.0155 Ω
- R_total = 1.15 Ω + 6.2 Ω = 7.35 Ω
6. Calculate the total copper loss on half of full load:
- Copper loss = (I1)^2 * R_total
- Copper loss = (20 A)^2 * 7.35 Ω
- Copper loss = 400 * 7.35 W
- Copper loss = 2940 W
Therefore, the total copper loss on half of full load is 2940 W or 2940/2 = 1470 W
The closest option to the calculated value is 214.2 W, which is the correct answer.
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A one-phase, 50 Hz, 40 kVA transformer with a ratio of 2000 V/250 V has a primary resistance of 1.15 Ω and a secondary resistance of 0.0155 Ω. Calculate total copper loss on half of the full load.a)856.8 Wb)214.2 Wc)642.6 Wd)428.4 WCorrect answer is option 'B'. Can you explain this answer?
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