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
The dot convention for a transformer states that the induced EMFs in the primary and secondary windings will have the same polarity at the dotted terminals.
1.Dot Convention Analysis: In Option (B), the primary dot is at the bottom and the secondary dot is at the top. The induced primary EMF is shown with a '+' at the bottom (dotted terminal), and the induced secondary EMF is shown with a '+' at the top (dotted terminal). This satisfies the dot convention as both induced voltages are positive at their respective dots.
2.Terminal Voltage Definitions: In a standard transformer model, the applied primary voltage is approximately equal to the induced primary EMF (), and the open-circuit secondary terminal voltage is equal to the induced secondary EMF (). In Option (B), is defined with the same polarity as , and is defined with the same polarity as .
3.Comparison with other options:
- In Option (A), is '+' at the top (no dot) while is '+' at the top (no dot, but dot is at bottom). This violates the dot convention.
- In Option (C), while the induced EMFs and satisfy the dot convention, the applied voltage is defined with opposite polarity to (), which is a non-standard representation.
- In Option (D), is '+' at the bottom (dot) while is '+' at the bottom (no dot). This violates the dot convention.
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