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Interest in numerical methods for solving electromagnetic field problems has in the last years set back the development of analytical methods. However, analytical methods can be advantageous in many cases and, as usual, give better insight to the solved problem. For this purpose a new analytical approach based on application of quaternions (hyper complex numbers) is presented in this paper.

In this paper an outline of the development of methods for the analysis of non‐linear circuits is presented. Non‐inert and inert elements have been discerned and an inertia measure has been proposed. For this purpose, an exponential function with time constant T equal to T_R, T_L, or T_C is formulated for an element of type R, L, or C, respectively. In circuits with the imposed cause, which varies sinusoidally in time with period T_e, the following situations are distinguished and considered: T_e ≫ T; T_e ≪ T; and T_e ≈ T. In the first case, the effect changes in time according to the non‐linear characteristic of the element. In the second case, the respective circuit is referred to as the “quasi‐linear”, because for the sinusoidal cause the effect is also sinusoidal. In the third case, the hysteresis occurs and the effect is a two‐valued function. The hysteresis effect occurs also in resistive elements.