Consider two transformers X and Y having exact ratings, but have flux densities of 1.5T and 2T respectively. The weight of the transformer A per KVA will bea)more than that of Bb)lesser than that of Bc)equal to that of Bd)can not be said from the given dataCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Transformer A vs Transformer B

The given problem states that two transformers X and Y have exact ratings, but have different flux densities. The weight per KVA of transformer A is to be compared with that of transformer B.

Transformer Weight and Flux Density

The weight of a transformer is directly proportional to its core area and the volume of copper used in the winding. The core area of a transformer is proportional to the square of the flux density. Thus, a higher flux density leads to a smaller core area and hence a smaller weight for the same KVA rating.

Mathematically, weight per KVA is given by:
Weight per KVA = (Volume of copper + Volume of core) / KVA rating
Volume of core = (Core area) x (Stack height)
Core area = (Flux density) x (Effective area)

Comparison of Transformers A and B

Transformer A has a flux density of 1.5T and transformer B has a flux density of 2T. Let us assume that both transformers have the same effective area and stack height.

- Core area: The core area of transformer A will be (1.5T) x (effective area), while that of transformer B will be (2T) x (effective area). As the effective area is the same for both transformers, the core area of transformer B will be higher.
- Volume of core: As the stack height is the same for both transformers, the volume of core will be proportional to the core area. Hence, the volume of core of transformer B will be higher.
- Weight per KVA: As the KVA rating is the same for both transformers, the weight per KVA will be proportional to the volume of copper + volume of core. As the volume of core of transformer B is higher, its weight per KVA will be higher.

Conclusion

Thus, we can conclude that transformer A will have a lower weight per KVA compared to transformer B, as it has a lower flux density. Hence, the correct answer is option 'A' - more than that of B.

Answer

Flux density = flux/ Area
Hence A has more area than B and so weight of A will be more than that of B

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