Multiple reactions in inductors

In this paper, the importance of the high-order nested (recursive) reactions that can take place in lossy inductors is investigated. The inquisitive student may ask, “What about the Faraday/Lenz reaction to the `first´ Faraday/Lenz reaction?”-a matter about which textbooks are generally silent. It is shown here that the sinusoidal steady-state results for the current in a lossy inductor normally obtained by solving differential equations or performing phasor calculations can be reproduced exactly using Faraday´s/Lenz´s laws recursively, to infinite order. Thus no knowledge of differential equations nor of phasors is required to find the current, and the result practically demonstrates the connection between Faraday´s/Lenz laws and circuit analysis. The case of a single sinusoid is analyzed, which by Fourier´s theorem and linear superposition can in principle be generalized to any excitation. Moreover, the dynamic equations developed can be used directly for any excitation without appeal to Fourier decomposition. A typical nonsinusoidal initial-value problem, involving both transient and driving-function components, is solved as a further demonstration of the technique