GATE EE 2024 Set 1 — Question 18
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Electrical Machines → Single-Phase Transformers → Polarity & Sumpner's Test
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Question
Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here, is the applied primary voltage, is the induced primary voltage, is the open circuit secondary voltage, and is the induced secondary voltage.
Correct answer
(B) [figure]
Solution
Both windings link the same mutual flux, so by the definition of the dot convention the induced emfs and must be positive at the dotted terminals at the same instant.Two conditions must therefore hold in a consistent diagram:
1. is marked '+' at the dotted primary terminal and is marked '+' at the dotted secondary terminal.
2.The source is applied to the primary, so the applied voltage has the same polarity as the induced primary voltage (); with the secondary open circuited no current flows, so the secondary terminal voltage equals the induced secondary voltage with the same polarity ().
Checking the options (in every option the primary dot is at the bottom terminal and the secondary dot at the top terminal):- (A) is '+' at the top, i.e. at the undotted primary terminal, while is '+' at the top, i.e. at the dotted secondary terminal. The two induced emfs are not positive at the dots together, so condition 1 fails.
- (C) is '+' at the bottom (dotted) terminal, but is '+' at the bottom, which is the undotted secondary terminal, so condition 1 fails. In addition is '+' at the top while is '+' at the bottom, i.e. , and is drawn opposite to , so condition 2 fails too.
- (D) Again is '+' at the dotted terminal while is '+' at the undotted terminal, so condition 1 fails, and is drawn opposite to .
- (B) is '+' at the bottom, which is the dotted primary terminal, and is '+' at the top, which is the dotted secondary terminal, so condition 1 holds. is marked with the same polarity as and with the same polarity as , so condition 2 holds as well.
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