A transformer has a primary winding of 800 turns and a secondary windi...
Problem: Finding the no-load current and its phase with respect to voltage in a transformer with given primary and secondary winding turns and load current.
Solution:
Step 1: Calculate the apparent power on the secondary side of the transformer.
Apparent power on the secondary side, S = V x I
where, V = voltage on the secondary side
and I = load current on the secondary side
Given load current on the secondary side, I = 80 A
Power factor on the secondary side, pf = 0.8 lagging
Hence, cos(φ) = 0.8 and sin(φ) = 0.6
Therefore, voltage on the secondary side, V = I / (pf x √3)
= 80 / (0.8 x √3) = 48.99 V
Apparent power on the secondary side, S = 48.99 x 80 = 3919.2 VA
Step 2: Calculate the apparent power on the primary side of the transformer.
Apparent power on the primary side, S = V x I
where, V = voltage on the primary side
and I = primary current
Given primary current, I = 25 A
Power factor on the primary side, pf = 0.707 lagging
Hence, cos(φ) = 0.707 and sin(φ) = 0.707
Therefore, voltage on the primary side, V = I / (pf x √3)
= 25 / (0.707 x √3) = 14.43 V
Apparent power on the primary side, S = 14.43 x 25 = 360.75 VA
Step 3: Calculate the no-load current of the transformer.
No-load current of the transformer, Io = S / V
where, S = apparent power on the primary side
and V = voltage on the primary side
Given S = 360.75 VA and V = 14.43 V
No-load current, Io = 360.75 / 14.43 = 24.99 A
Step 4: Determine the phase of the no-load current with respect to voltage.
The no-load current of a transformer lags the voltage by a small angle due to the magnetization of the core. This angle is usually denoted by θ or φ.
Given primary current, I = 25 A
Power factor on the primary side, pf = 0.707 lagging
Hence, cos(φ) = 0.707 and sin(φ) = 0.707
The no-load current of a transformer is purely reactive, i.e., it has no real power component. Therefore, the power factor of the no-load current is zero.
Hence, the phase of the no-load current with respect to voltage is purely reactive and lags the voltage by an angle θ or φ.
To make sure you are not studying endlessly, EduRev has designed Railways study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Railways.