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In a single-phase transformer, the total iron loss is 2500 W at nomina;l voltage of 440 V and frequency 50 Hz. The total iron loss is 850 W at 220 V and 25 Hz. Then, at nominal voltage and frequency, the hystersis and eddy current loss respectively are
- a)250 W and 600 W
- b)900 W and 1600 W
- c)1600 W and 900 W
- d)600 W and 250 W
Correct answer is option 'B'. Can you explain this answer?
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In a single-phase transformer, the total iron loss is 2500 W at nomina...
Given Information:
- Total iron loss in a single-phase transformer is 2500 W at a nominal voltage of 440 V and frequency of 50 Hz.
- Total iron loss is 850 W at a voltage of 220 V and frequency of 25 Hz.
To Find:
The hysteresis and eddy current loss at the nominal voltage and frequency.
Solution:
1. Hysteresis Loss:
Hysteresis loss is dependent on the magnetic properties of the transformer core material and the frequency of operation. It is given as:
P_h = k_h × f × B^1.6 × V^2
Where,
P_h = Hysteresis loss
k_h = Hysteresis constant
f = Frequency
B = Magnetic flux density
V = Voltage
We can write the equation for hysteresis loss at two different voltages and frequencies:
P_h1 = k_h × f1 × B^1.6 × V1^2 ...(1)
P_h2 = k_h × f2 × B^1.6 × V2^2 ...(2)
Dividing equation (2) by equation (1), we get:
P_h2/P_h1 = (k_h × f2 × B^1.6 × V2^2) / (k_h × f1 × B^1.6 × V1^2)
Since the magnetic flux density (B) and hysteresis constant (k_h) are the same for both equations, we can cancel them out:
P_h2/P_h1 = (f2 × V2^2) / (f1 × V1^2)
Given:
P_h1 = 2500 W
V1 = 440 V
f1 = 50 Hz
P_h2 = 850 W
V2 = 220 V
f2 = 25 Hz
Substituting the values into the equation:
850/2500 = (25 × 220^2) / (50 × 440^2)
Simplifying the equation:
1/2.94 = (25 × 220^2) / (50 × 440^2)
Solving for (25 × 220^2) / (50 × 440^2), we get:
(25 × 220^2) / (50 × 440^2) = 0.5
Therefore, the hysteresis loss at nominal voltage and frequency is:
P_h = P_h1 × 0.5 = 2500 × 0.5 = 1250 W
2. Eddy Current Loss:
Eddy current loss is caused by circulating currents induced in the conducting parts of the transformer core due to varying magnetic fields. It is given by:
P_e = k_e × f × B^2 × t^2 × V^2
Where,
P_e = Eddy current loss
k_e = Eddy current constant
f = Frequency
B = Magnetic flux density
t = Thickness of the laminations in the core
V = Voltage
Similar to the hysteresis loss, we can write the equation for eddy current loss at two different voltages and frequencies:
P_e1 = k_e × f1 × B^2 × t1
- Total iron loss in a single-phase transformer is 2500 W at a nominal voltage of 440 V and frequency of 50 Hz.
- Total iron loss is 850 W at a voltage of 220 V and frequency of 25 Hz.
To Find:
The hysteresis and eddy current loss at the nominal voltage and frequency.
Solution:
1. Hysteresis Loss:
Hysteresis loss is dependent on the magnetic properties of the transformer core material and the frequency of operation. It is given as:
P_h = k_h × f × B^1.6 × V^2
Where,
P_h = Hysteresis loss
k_h = Hysteresis constant
f = Frequency
B = Magnetic flux density
V = Voltage
We can write the equation for hysteresis loss at two different voltages and frequencies:
P_h1 = k_h × f1 × B^1.6 × V1^2 ...(1)
P_h2 = k_h × f2 × B^1.6 × V2^2 ...(2)
Dividing equation (2) by equation (1), we get:
P_h2/P_h1 = (k_h × f2 × B^1.6 × V2^2) / (k_h × f1 × B^1.6 × V1^2)
Since the magnetic flux density (B) and hysteresis constant (k_h) are the same for both equations, we can cancel them out:
P_h2/P_h1 = (f2 × V2^2) / (f1 × V1^2)
Given:
P_h1 = 2500 W
V1 = 440 V
f1 = 50 Hz
P_h2 = 850 W
V2 = 220 V
f2 = 25 Hz
Substituting the values into the equation:
850/2500 = (25 × 220^2) / (50 × 440^2)
Simplifying the equation:
1/2.94 = (25 × 220^2) / (50 × 440^2)
Solving for (25 × 220^2) / (50 × 440^2), we get:
(25 × 220^2) / (50 × 440^2) = 0.5
Therefore, the hysteresis loss at nominal voltage and frequency is:
P_h = P_h1 × 0.5 = 2500 × 0.5 = 1250 W
2. Eddy Current Loss:
Eddy current loss is caused by circulating currents induced in the conducting parts of the transformer core due to varying magnetic fields. It is given by:
P_e = k_e × f × B^2 × t^2 × V^2
Where,
P_e = Eddy current loss
k_e = Eddy current constant
f = Frequency
B = Magnetic flux density
t = Thickness of the laminations in the core
V = Voltage
Similar to the hysteresis loss, we can write the equation for eddy current loss at two different voltages and frequencies:
P_e1 = k_e × f1 × B^2 × t1
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Community Answer
In a single-phase transformer, the total iron loss is 2500 W at nomina...
Wi1 = 2500 W at 440 V, 50 Hz
Wi2 = 850 W at 220 V, 25 Hz
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In a single-phase transformer, the total iron loss is 2500 W at nomina;l voltage of 440 V and frequency 50 Hz. The total iron loss is 850 W at 220 V and 25 Hz. Then, at nominal voltage and frequency, the hystersis and eddy current loss respectively area)250 W and 600 Wb)900 W and 1600 Wc)1600 W and 900 Wd)600 W and 250 WCorrect answer is option 'B'. Can you explain this answer?
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