Clarifying concepts and gaining a deeper understanding of ideal transformers

Even in ideal transformers, the input and output powers are never exactly equal, thereby causing the familiar ratio between the primary and secondary currents, namely I _p :I _s = N _s :N _p, to be slightly incorrect. In this paper, we explain why this is so and derive the correct ratio, as well as clarifying the related prevailing concepts. We conclude that a theory of an ideal transformer without a magnetising current is deficient and self-contradictory. Further, methods to locate the two black (phase) dots in a transformer symbol are elucidated. This paper is suitable for those who are pursuing a deeper understanding on this subject after learning the basics from the literature. (paper)