Variational alternatives to Kirchhoff's loop theorem in dc circuits

American Journal of Physics

Volumn 67, Issue 1, 1999, Pages 36-44

  Van Baak, D A ^a  

^a CALVIN COLLEGE   (United States)

Author keywords

41; 84

Indexed keywords

EID: 22444456124     PISSN: 00029505     EISSN: 19432909     Source Type: Journal    
DOI: 10.1119/1.19188     Document Type: Article

References (5)

1. “As an example, if currents are made to go through a piece of material obeying Ohm's law, the currents distribute themselves inside the piece so that the rate at which heat is generated is as little as possible.” R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison–Wesley, Reading, MA, 1964), Vol. 2, Chap. 19 (The Principle of Least Action: A special lecture—almost verbatim), in “A note added after the lecture.”
2. J. C. Maxwell, A Treatise on Electricity and Magnetism (Dover, New York, 1954, reprint of the 3rd ed. of 1891), Vol. 1; Articles 283–284 state and prove the theorem “In any system of conductors in which there are no internal electromotive forces the heat generated by currents distributed in accordance with Ohm's Law is less than if the currents had been distributed in any other manner consistent with the actual conditions of supply and outflow of the current.”
3. David J. Griffiths, Introduction to Electrodynamics, 2nd ed. (Prentice–Hall, Englewood Cliffs, NJ, 1989), Chap. 7.1.2.
4. W. M. Saslow, “Consider a spherical battery…,” Am. J. Phys. AJPIAS 62, 495–501 (1994).
5. Don S. Lemons, Perfect Form (Princeton U.P., Princeton, NJ, 1997).