Kirchhoff’s Third and Fourth Laws
Consider a connected resistive network energized exclusively by current sources or exclusively by voltage sources. In Chapter Seven we have established the existence and uniqueness of a current chain and a voltage chain describing the performance of the network and satisfying Ohm’s Law and Kirchhoff’s Voltage Law and Kirchhoff’s Current Law. However, we pointed out that the formulas developed in Chapter Seven for the current chain and voltage chain are not suitable for specific calculation of the branch currents and the branch voltages. In this Chapter we develop additional formulas for the current chain and voltage chain from which the branch currents and branch voltages may be readily calculated. We conclude this Chapter by showing that these formulas are essentially invariant under changes in the orientation of the branches of the network.
KeywordsCurrent Source Voltage Source Preceding Theorem Resistive Network Branch Current
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- Arsove, M. G.: A Note on the Network Postulates. Journal of Mathematics and Physics. 32, 1953.Google Scholar
- Bayard, M. Theorie des Reseaux de Kirchhoff. La Revue d’Optique, Paris, 1954.Google Scholar
- Cauer, W.: Synthesis of Linear Communication Networks. Translated by G. E. Knausenberger and J. N. Warfield. New York: McGraw-Hill 1958.Google Scholar
- Harary, F.: Graph Theory and Electric Networks. IRE Trans. on Circuit Theory, special supplement, CT-6, May, 1959.Google Scholar
- Kirchhoff, G.: On the Solution of the Equations Obtained from the Investigation of the Linear Distribution of Galvanic Currents. Translated by J. B. O’Toole. IRE Trans. on Circuit Theory, CT-5, March, 1958.Google Scholar
- MacWilliams, F. J.: An Algebraic Proof of Kirchhoff’s Network Theorem. Bell Telephone Laboratories, internal memorandum, Murray Hill, New Jersey, Oct. 22, 1958.Google Scholar
- Nerode, A., and H. Shank: Topological Network Theory. WADC Technical Report 57–424, Astia Document Number AD 155730, Wright Air Development Center, November, 1957.Google Scholar
- Reza, F. M.: Some Topological Considerations in Network Synthesis. IRE Trans, on Circuit Theory, CT-5, March, 1958.Google Scholar
- Tellegen, B. D. H.: Theorie der Electrischen Netwerken. In Elias, G. J., and B. D. H. Tellegen: Theorie der Wechselstrommen, vol. 3. Groningen, Djakarta: P. Noordhoff N. V. 1952.Google Scholar
- Weinberg, L.: Kirchhoff’s Third and Fourth Laws. IRE Trans. on Circuit Theory, CT-5, March, 1958.Google Scholar
- Weinberg, L.: Network Analysis and Synthesis. New York: McGraw-Hill 1962.Google Scholar