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A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).
Correct answer is '162.50'. Can you explain this answer?
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Verified Answer
A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated C...
200 V, 50 Hz, Pc = 450 Watt
160 V, 40 Hz, Pc = 320 Watt
100 V, 25 Hz, Pc = ? Watt
So, Pc = Af + Bf2
450 = A × (50) + B × (50)2 ...(i)
320 = A × (40) + B × (40)2 ...(ii)
From (i) and (ii),
...(iii)
320/40 = A + B(40) ...(iv)
Equation (iii) – (iv),
(9 – 8) = B(10)
B = 1/10
and A = 9 - (1/10) x 50 = 4
Now at 100 V, 25 Hz, Pc = 4 x 25 + (1/10) x (25)2
= 100 + 62.5 = 162.50 Watt
160 V, 40 Hz, Pc = 320 Watt
100 V, 25 Hz, Pc = ? Watt
So, Pc = Af + Bf2
450 = A × (50) + B × (50)2 ...(i)
320 = A × (40) + B × (40)2 ...(ii)
From (i) and (ii),
...(iii)320/40 = A + B(40) ...(iv)
Equation (iii) – (iv),
(9 – 8) = B(10)
B = 1/10
and A = 9 - (1/10) x 50 = 4
Now at 100 V, 25 Hz, Pc = 4 x 25 + (1/10) x (25)2
= 100 + 62.5 = 162.50 Watt
Most Upvoted Answer
A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated C...
Given Data:
- Rated power of the transformer (S) = 4 kVA
- Rated voltage of the high-voltage winding (V1) = 200 V
- Rated voltage of the low-voltage winding (V2) = 100 V
- Rated frequency (f) = 50 Hz
- Rated no-load loss (P0) = 450 W
- No-load loss at 160 V, 40 Hz (P1) = 320 W
Step 1: Calculation of Rated Current
The rated current (I1) can be calculated using the formula:
I1 = S / V1
= 4000 VA / 200 V
= 20 A
Step 2: Calculation of Rated Flux Density
The rated flux density (B0) can be calculated using the formula:
B0 = √(P0 / (4.44 * f * A))
= √(450 / (4.44 * 50 * 0.001))
= √(450 / 0.222)
= √2027.03
= 45.05 T
Step 3: Calculation of Rated Magnetizing Current
The rated magnetizing current (Im0) can be calculated using the formula:
Im0 = (P0 / V1)
= 450 W / 200 V
= 2.25 A
Step 4: Calculation of No-load Reactance
The no-load reactance (X0) can be calculated using the formula:
X0 = V1 / Im0
= 200 V / 2.25 A
= 88.89 Ω
Step 5: Calculation of No-load Impedance
The no-load impedance (Z0) can be calculated using the formula:
Z0 = √(R0^2 + X0^2)
= √(0^2 + 88.89^2)
= 88.89 Ω
Step 6: Calculation of Frequency Ratio
The frequency ratio (f1) can be calculated using the formula:
f1 = f1 / f
= 40 Hz / 50 Hz
= 0.8
Step 7: Calculation of No-load Loss at 100 V, 25 Hz
The no-load loss at 100 V, 25 Hz (P2) can be calculated using the formula:
P2 = P1 * (V2 / V1)^2 * (f1 / f)
= 320 W * (100 V / 200 V)^2 * (0.8 / 1)
= 320 W * (0.5)^2 * 0.8
= 320 W * 0.25 * 0.8
= 64 W
Final Answer:
The no-load losses at 100 V, 25 Hz are 64 W, rounded off to 2 decimal places.
- Rated power of the transformer (S) = 4 kVA
- Rated voltage of the high-voltage winding (V1) = 200 V
- Rated voltage of the low-voltage winding (V2) = 100 V
- Rated frequency (f) = 50 Hz
- Rated no-load loss (P0) = 450 W
- No-load loss at 160 V, 40 Hz (P1) = 320 W
Step 1: Calculation of Rated Current
The rated current (I1) can be calculated using the formula:
I1 = S / V1
= 4000 VA / 200 V
= 20 A
Step 2: Calculation of Rated Flux Density
The rated flux density (B0) can be calculated using the formula:
B0 = √(P0 / (4.44 * f * A))
= √(450 / (4.44 * 50 * 0.001))
= √(450 / 0.222)
= √2027.03
= 45.05 T
Step 3: Calculation of Rated Magnetizing Current
The rated magnetizing current (Im0) can be calculated using the formula:
Im0 = (P0 / V1)
= 450 W / 200 V
= 2.25 A
Step 4: Calculation of No-load Reactance
The no-load reactance (X0) can be calculated using the formula:
X0 = V1 / Im0
= 200 V / 2.25 A
= 88.89 Ω
Step 5: Calculation of No-load Impedance
The no-load impedance (Z0) can be calculated using the formula:
Z0 = √(R0^2 + X0^2)
= √(0^2 + 88.89^2)
= 88.89 Ω
Step 6: Calculation of Frequency Ratio
The frequency ratio (f1) can be calculated using the formula:
f1 = f1 / f
= 40 Hz / 50 Hz
= 0.8
Step 7: Calculation of No-load Loss at 100 V, 25 Hz
The no-load loss at 100 V, 25 Hz (P2) can be calculated using the formula:
P2 = P1 * (V2 / V1)^2 * (f1 / f)
= 320 W * (100 V / 200 V)^2 * (0.8 / 1)
= 320 W * (0.5)^2 * 0.8
= 320 W * 0.25 * 0.8
= 64 W
Final Answer:
The no-load losses at 100 V, 25 Hz are 64 W, rounded off to 2 decimal places.
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A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).Correct answer is '162.50'. Can you explain this answer?
Question Description
A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).Correct answer is '162.50'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).Correct answer is '162.50'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).Correct answer is '162.50'. Can you explain this answer?.
A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).Correct answer is '162.50'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).Correct answer is '162.50'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________W (rounded off to 2 decimal places).Correct answer is '162.50'. Can you explain this answer?.
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