GATE EE 2025 Set 1 — Question 43
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Electrical Machines → Three-Phase Transformers → Connections & Vector Groups
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Question
The transformer connection given in the figure is part of a balanced 3-phase circuit where the phase sequence is “abc”. The primary to secondary turns ratio is 2:1. If , then the relationship between and will be
Correct answer
(A) I_A I_(ad) = 12√(3) and I_(ad) lags I_A by 30^.
Solution
1.Primary Side (Star Connection):
The primary is star-connected, so the line current is equal to the phase current in the primary winding of Leg 1.2.Secondary Side (Zig-zag Connection):
In a zig-zag connection, each phase current is formed by the difference of currents in two windings from different legs. From the diagram, the line current flows through the top winding of Leg 1 and the bottom winding of Leg 2. Let be the primary turns and be the turns of each secondary winding. The given turns ratio is .
3.Ampere-Turn Balance:
For Leg 1, the ampere-turn balance equation (considering dot conventions for a standard zig-zag transformer) is:4.Phasor Analysis:
For a balanced sequence, let . Then .Substituting the turns ratio :
This implies and lags by .
5.Conclusion:
Based on the specific definition of turns ratio and connection details intended in the problem, the magnitude ratio is and lags by .Continue learning with Success Tracker
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