The Bell System Technical Journal 



January^ 1927 



Electromagnetic Theory and the Foundations of Electric 



Circuit Theory ^ 



By JOHN R. CARSON 



Synopsis: The familiar equations which are used to solve for the currents 

 and charges in linear networks summarize the inductive analysis of countless 

 observations made upon such networks. Having been arrived at by induc- 

 tive methods, these familiar equations of Ohm, Faraday and Kirchhoff 

 are substantially independent of the more general electromagnetic theory 

 of Maxwell and Lorentz. The present paper examines the foundation of 

 electric circuit theory from the standpoint of the fundamental equations of 

 electromagnetic theory and a derivation of the former from the latter is 

 made, in the course of which the assumptions, approximations and restric- 

 tions tacitly involved in the equations of circuit theory are explicitly stated. 

 The treatment is sufficiently extended as to show how the familiar equation 

 for the simple oscillating circuit and the so-called telegraph equation can 

 be deduced from the Maxwell-Lorentz statement of electromagnetic theory. 



ELECTRIC circuit theory, as the term is employed in the present 

 paper, is that branch of electromagnetic theory which deals with 

 electrical oscillations in linear networks; more precisely stated, with 

 the distribution of currents and charges in the free oscillations of the 

 network, or under the action of impressed electromotive forces. The 

 network is a connected set of closed circuits or meshes each of which 

 is regarded as made up of inductances, resistances and condensers, a 

 simplifying assumption which is fundamental to circuit theory. 



The great importance of electric circuit theory in electro-technics 

 does not require emphasis; it is not too much to say that it is respon- 

 sible in no small measure for the rapid development of electrical 

 engineering and is an absolutely essential guide in the complicated 

 technical problems there encountered. 



The equations of electric circuit theory in their present form are 

 essentially a generalization of the observations of Ohm, Faraday, 

 Henry, Kirchhoff and others and their development preceded the 

 electromagnetic theory of Maxwell and Lorentz. Naturally, in view 

 of its early development, circuit theory embodies approximations, 

 the precision of which cannot be determined from the observations on 

 which it is based. For example, circuit theory explicitly ignores the 

 finite velocity of propagation of electromagnetic disturbances, and 



^ In its original form this paper was read before the National Academy of Sciences, 

 April 1925. Subsequently it was amplified and revised and included in a lecture 

 course delivered at the Massachusetts Institute of Technology, April 1926. 

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