Select the option that is correct regarding the following two statements labelled Assertion (A) and Reason (R). Assertion (A): Three-phase auto-transformers are smaller and lighter than equivalent three-phase two-winding transformers. Reason (R): Auto-transformers use fewer windings and a smaller core.
Both A and R are true, and R is the correct explanation of A.
Let's analyze the given statements to determine their correctness and how they relate to each other:
- Assertion (A): "Three-phase auto-transformers are smaller and lighter than equivalent three-phase two-winding transformers."
- Reason (R): "Auto-transformers use fewer windings and a smaller core."
Explanation:
- In a three-phase auto-transformer, the primary and secondary windings are electrically connected, sharing common windings. This design requires fewer materials: less copper for the windings and a smaller iron core, as the core needs to accommodate only the extra voltage transformation portion.
- On the other hand, traditional two-winding transformers have separate primary and secondary windings. This necessitates more materials and results in a larger and heavier structure compared to an auto-transformer of equivalent power rating.
- Therefore, the assertion correctly states that auto-transformers are smaller and lighter due to this reduced material requirement.
Conclusion: Both the Assertion (A) and Reason (R) are true, and the reason provided is indeed the correct explanation for the assertion. The auto-transformer's design inherently requires fewer windings and a smaller core than what is needed in a conventional transformer setup, thus making it smaller and lighter.
Therefore, the correct answer is: Both A and R are true, and R is the correct explanation of A.
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