Explanation (or Proof) for network theorems?

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SUMMARY

This discussion focuses on the foundational network theorems used in circuit analysis, specifically Kirchhoff's Laws (KVL and KCL), Source Transformation, Superposition Theorem, Thevenin's Theorem, Norton's Theorem, and Star-Delta Conversion. The participants express a need for proofs of these theorems, questioning whether they are derived from empirical methods or higher mathematics. It is established that while some theorems can be intuitively understood through principles like energy conservation, their rigorous derivation often relies on mathematical frameworks, particularly Maxwell's equations and charge conservation.

PREREQUISITES
  • Understanding of Kirchhoff's Laws (KVL and KCL)
  • Familiarity with circuit analysis techniques
  • Basic knowledge of Maxwell's equations
  • Concept of charge conservation in electrical circuits
NEXT STEPS
  • Research the mathematical derivation of Kirchhoff's Laws from Maxwell's equations
  • Study the proofs of the Superposition Theorem in circuit analysis
  • Explore the applications and derivations of Thevenin's and Norton's Theorems
  • Learn about Star-Delta Conversion and its implications in circuit design
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in deepening their understanding of network theorems and their mathematical foundations.

ArchKudo
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We started Network analysis and we were given Circuit Diagrams to be reduced using the following:
  1. Kirchoff's Laws i.e KVL and KCL
  2. Source Transformation
  3. Superposition Theorem
  4. Thevenin's Theorem
  5. Norton's Theorem and
  6. Star-Delta Conversion
However I wasn't given proofs for any of these theorem just their application (which is really easy) and now, I can't find their proofs on the internet too!
So, are these theorems based on empirical method or do they use higher mathematics?
And if not it would be great if someone could provide me with their proofs

ps: I can guess why some theorems are true like KVL or KCL because of energy conservation I suppose and Superposition theorem is relate-able to Superposition of electric fields and its relation with electric potentional but it is still confusing
 
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They all can be derived from the Maxwell equations and charge conservation, those two are based on experiments. Introductory textbooks on electrostatics and circuits might cover that in more or less detail. Getting Kirchhoff's laws out of them is not so straight forward, getting the others from those laws is mainly mathematics.
 
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