About this paper

Appears in:
Pages: 7981-7987
Publication year: 2018
ISBN: 978-84-09-05948-5
ISSN: 2340-1095
doi: 10.21125/iceri.2018.0431

Conference name: 11th annual International Conference of Education, Research and Innovation
Dates: 12-14 November, 2018
Location: Seville, Spain

DIDACTIC MATHEMATICAL DERIVATION OF THE REAL AND IDEAL TRANSFORMER MODELS

J. Gonzalez

SUNY New Paltz (UNITED STATES)
This paper presents a potential solution to a pedagogic deficiency in current textbooks on Electric Circuits Theory. Most textbooks on this discipline, extensively address the topic of magnetically coupled coils using phasors. However, when covering the concept of an ideal transformer, these textbooks define it in terms of voltage and current conversions, without establishing a clear logical connection with magnetically coupled circuit theory. This lack of clear connection deprives students from obtaining a deep understanding of transformers.

In this paper, we first establish the general equations for two magnetically coupled coils, the primary and the secondary. Then, we consider six possible solutions to these equations, and adopt the solution that best meets our need to describe power transmission from primary to secondary. A topological interpretation of this solution under Kirchhoff’s laws provides a useful model for the real transformer. By considering ideal conditions, we show how the model of the real transformer becomes the model for the ideal transformer. This way, we derive- rather than simply define- the conversion relationships that exist between a transformer primary and secondary voltages and currents. Such an approach can better support students in developing strong understandings of this subject matter.

Finally, this paper assesses student learning to show how students’ understanding benefits from a logical derivation that connects magnetically coupled circuit theory to the real and ideal transformer models.
@InProceedings{GONZALEZ2018DID,
author = {Gonzalez, J.},
title = {DIDACTIC MATHEMATICAL DERIVATION OF THE REAL AND IDEAL TRANSFORMER MODELS},
series = {11th annual International Conference of Education, Research and Innovation},
booktitle = {ICERI2018 Proceedings},
isbn = {978-84-09-05948-5},
issn = {2340-1095},
doi = {10.21125/iceri.2018.0431},
url = {http://dx.doi.org/10.21125/iceri.2018.0431},
publisher = {IATED},
location = {Seville, Spain},
month = {12-14 November, 2018},
year = {2018},
pages = {7981-7987}}
TY - CONF
AU - J. Gonzalez
TI - DIDACTIC MATHEMATICAL DERIVATION OF THE REAL AND IDEAL TRANSFORMER MODELS
SN - 978-84-09-05948-5/2340-1095
DO - 10.21125/iceri.2018.0431
PY - 2018
Y1 - 12-14 November, 2018
CI - Seville, Spain
JO - 11th annual International Conference of Education, Research and Innovation
JA - ICERI2018 Proceedings
SP - 7981
EP - 7987
ER -
J. Gonzalez (2018) DIDACTIC MATHEMATICAL DERIVATION OF THE REAL AND IDEAL TRANSFORMER MODELS, ICERI2018 Proceedings, pp. 7981-7987.
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