An audio product company needs a 50 Hz step down transformer with 125 kVA power in the primary winding. The voltage ratio of the transformer is 1100/220 V with 120 turns on its sec... An audio product company needs a 50 Hz step down transformer with 125 kVA power in the primary winding. The voltage ratio of the transformer is 1100/220 V with 120 turns on its secondary winding. Calculate the number of turns of the primary winding and the currents that would flow in both the windings when fully loaded.
Understand the Problem
The question is asking to calculate the number of turns in the primary winding of a transformer and the currents that will flow in both windings when it is fully loaded, given certain parameters including power and voltage ratio.
Answer
The primary winding has \( N_p = 600 \) turns, with \( I_s \approx 568.18 \, A \) (secondary) and \( I_p \approx 113.64 \, A \) (primary).
Answer for screen readers
The number of turns in the primary winding is ( N_p = 600 ) turns. The currents flowing in the windings when fully loaded are ( I_s \approx 568.18 , A ) (secondary) and ( I_p \approx 113.64 , A ) (primary).
Steps to Solve
- Calculate the Turns Ratio The turns ratio of the transformer can be found using the voltage ratio. Given that the primary voltage ( V_p = 1100 , V ) and the secondary voltage ( V_s = 220 , V ), the turns ratio ( n ) is given by:
[ n = \frac{V_p}{V_s} = \frac{1100}{220} = 5 ]
- Calculate the Number of Turns in the Primary Winding The number of turns in the primary winding can be calculated using the turns ratio and the known secondary turns. Let ( N_s = 120 ) (turns in the secondary). The formula is:
[ N_p = n \times N_s = 5 \times 120 = 600 ]
- Determine the Current in the Secondary Winding First, we calculate the apparent power ( S ) in VA:
[ S = 125 , kVA = 125000 , VA ]
Next, calculate the secondary current ( I_s ) using the formula:
[ I_s = \frac{S}{V_s} ]
Substituting the values:
[ I_s = \frac{125000}{220} \approx 568.18 , A ]
- Determine the Current in the Primary Winding Using the transformer current relationship, we can find the primary current ( I_p ):
[ I_p = \frac{I_s}{n} ]
Substituting the values:
[ I_p = \frac{568.18}{5} \approx 113.64 , A ]
The number of turns in the primary winding is ( N_p = 600 ) turns. The currents flowing in the windings when fully loaded are ( I_s \approx 568.18 , A ) (secondary) and ( I_p \approx 113.64 , A ) (primary).
More Information
Transformers are essential in electrical systems, converting voltage levels while maintaining power. The turns ratio directly impacts the current in both windings.
Tips
- Not accounting for the power factor when calculating currents: This problem assumes a purely resistive load for simplicity.
- Confusing the roles of primary and secondary voltages, which can lead to incorrect calculations of turns and currents.
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