Abstract
The history of the concept of phasor is often neglected when it is introduced in textbooks on circuits. The presentation does not emphasize the historical aspects, which is natural. This paper intends to recover the original and creative way the concept of complex numbers, then almost unknown to engineers, was applied to electric circuits in sinusoidal steady-state. As usual in physics and engineering, the theory of phasor could have been anticipated by earlier researchers, if they had followed their original reasonings. Maxwell and Heaviside had proved the meal, but could not, or were not interested in writing the recipe.
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Notes
All non-trivial solution of the Laplace’s Equation—a partial differential equation represented by \(\nabla ^2 u = 0\)—is called harmonic function. Trigonometric functions are examples of harmonic functions.
For a description about the contribution of Wessel for the complex analysis, see first chapter of Crowe (1985).
A link between the works of Fourier, Laplace, and Heaviside is presented in Tonidandel and Araújo (2012a).
Fourier considers also the planes \(B\) and \(C\) subjected to a constant temperature (zero).
Analisys which, by the way, anticipates in one decade the discovery of the fundamental equations of electromagnetism, the Maxwell’s Equations.
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Araújo, A.E.A., Tonidandel, D.A.V. Steinmetz and the Concept of Phasor: A Forgotten Story. J Control Autom Electr Syst 24, 388–395 (2013). https://doi.org/10.1007/s40313-013-0030-5
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DOI: https://doi.org/10.1007/s40313-013-0030-5