Solving Series Transformers Problem with Lumped Resistance

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SUMMARY

The discussion addresses the complexities of analyzing current measurements in a system involving two toroidal current transformers (CTs) with a 50:5 nominal turn ratio and differing primary turns (15 and 5). The author highlights the need to consider both lumped wire resistance and complex models to accurately assess the behavior of the transformers. Key insights include the application of Kirchhoff's Voltage Law (KVL) and the importance of transformer efficiency, which is influenced by frequency, windings, and core material.

PREREQUISITES
  • Understanding of transformer theory, specifically turns ratio and magnetic coupling.
  • Familiarity with Kirchhoff's Voltage Law (KVL) and its application in circuit analysis.
  • Knowledge of lumped resistance concepts in electrical circuits.
  • Basic principles of transformer efficiency and its dependence on frequency and core material.
NEXT STEPS
  • Research the impact of transformer efficiency on current measurements in electrical systems.
  • Explore advanced modeling techniques for analyzing transformers, including finite element analysis.
  • Study the effects of core material on transformer performance and efficiency.
  • Learn about the dot convention in transformer analysis and its implications for circuit behavior.
USEFUL FOR

Electrical engineers, circuit designers, and students studying transformer theory who are interested in optimizing current measurement accuracy in transformer systems.

MRKN
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This is a problem I stumbled upon after noticing a pattern in the lab- the measured current was never quite what you'd expect from the turns ratio of either transformer alone, but somewhere in the middle.

I used 50:5 nominal turn toroidal CTs with 15 turns in one CT primary and 5 turns in the other primary.

This is not a homework question but rather an inquiry as far as whether or not I'd need to use complex models to analyze this situation, or rather lumped wire resistance.

To get a good start, notice the opposition of KVL in the secondary with the dot convention. This suggests zero flux in the transformer with the lesser amount of turns and thus simply Is = N1(Ip).
 

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Cannot be answered without knowing transformer efficiency (function of frequency, windings, core material).

An average current would be expected if the two transformers were magnetically coupled and behaving as one large transformer. Cheesy E-lams at 50-60Hz have a huge field...
 
you can find at basic electronic and tutorial..
 

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