A straightforward deduction of the electric circuit power Massimo Guarnieri Department of Electrical Engineering, University of Padua, Padova, Italy Abstract Purpose – The paper seeks to do the following. To provide an expression of the electromagnetic power flow that is alternative to the Poynting’s theorem expression, overcomes its postulate feature, and is particularly suitable for electric circuit elements. Design/methodology/approach – The paper proceeds from fundamental electromagnetic laws and, independently of Poynting’s formulation, follows an approach that generalize established double formulations of the electrostatic and magnetostatic energies. Findings – The paper proposes a compact and straightforward expression of the electromagnetic power flow based on the fundamental electromagnetic field sources, i.e. charge and current densities. Practical implications – The achieved expression confirms Poynting’s expression in the case of electric elements, overcoming its arbitrariness, generalizes previous partial results by other authors, deduced via the Poynting’s power balance. Originality/value – Is promising in the computation of power flow electromagnetic devices connected in electrical circuits, i.e. for coupled problems where the analysis of electromagnetic system interfaced to electric circuits is required. Due to its simple structure and straightforward deduction it has educational value to demonstrate the expressions of the electric power in circuit elements. Keywords Electromagnetism, Circuits Paper type Conceptual paper 1. Introduction Axiomatic approaches to circuit theory postulated the expression of the electric power through a circuit port: p ¼ vi ð1Þ with v and i the port voltage and current, respectively. This is the case in some textbooks, such as the established book by Chua et al. (1987) and it is a convenient choice as far as no demonstration is needed. On the other hand, an electromagnetic derivation of the port power, which is popular with many authors (Dorf and Svoboda, 2001; Nilsson and Riedel, 2005; Thomas and Rosa, 1998) considers the identity: p ¼ dw dt ¼ dw dq dq dt ð2Þ with w the electric energy flow (more correctly, the electrical work) and q the electric charge. At an accurate insight, equation (2) presents some consistency problems. In fact: . charges do not move necessarily from one port terminal to the other inside a multi-port element; The current issue and full text archive of this journal is available at www.emeraldinsight.com/0332-1649.htm Electric circuit power 1271 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 30 No. 4, 2011 pp. 1271-1282 q Emerald Group Publishing Limited 0332-1649 DOI 10.1108/03321641111133181