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The voltage applied to the primary winding of an unloaded single-phase transformer is given by
v=400cos⁡αt+100cos⁡3αt
The primary has 500 turns and frequency of the fundamental component of the applied voltage is 50Hz. What is the maximum value of flux in mWb is ________
  • a)
    2.3
  • b)
    2.334
Correct answer is between '2.3,2.334'. Can you explain this answer?
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The voltage applied to the primary winding of an unloaded single-phas...
To determine the maximum value of flux in a single-phase transformer, we need to find the maximum value of the magnetizing current. The magnetizing current is the current flowing through the primary winding when the transformer is unloaded.

Given:
Voltage applied to the primary winding, v = 400cos(αt) + 100cos(3αt)
Number of turns in the primary winding, N1 = 500
Frequency of the fundamental component of the applied voltage, f = 50 Hz

To find the maximum value of flux, we can use the formula:

Flux = (Vp * T) / (4 * f * N1)

Where:
Vp is the peak value of the applied voltage
T is the period of the fundamental component of the applied voltage

Finding the peak value of the applied voltage:
The peak value of a cosine function is equal to the amplitude of the function. In this case, the amplitude is 400 for the first term and 100 for the second term. Therefore, the peak value of the applied voltage is 400 + 100 = 500 V.

Finding the period of the fundamental component of the applied voltage:
The period is the reciprocal of the frequency, T = 1 / f = 1 / 50 = 0.02 seconds.

Using the formula for flux, we can substitute the values:

Flux = (500 * 0.02) / (4 * 50 * 500) = 0.01 / 100 = 0.0001 Wb

Converting the flux to milliwebers (mWb):
1 Wb = 1000 mWb
Therefore, the flux in milliwebers is 0.0001 * 1000 = 0.1 mWb.

However, the options provided are between 2.3 mWb and 2.334 mWb, which are significantly higher than the calculated value. It is possible that there is a mistake in the given equation or the options provided.
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The voltage applied to the primary winding of an unloaded single-phase transformer is given byv=400cos⁡αt+100cos⁡3αtThe primary has 500 turns and frequency of the fundamental component of the applied voltage is 50Hz. What is the maximum value of flux in mWb is ________a)2.3b)2.334Correct answer is between '2.3,2.334'. Can you explain this answer?
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