Outline of theory of impulse currents

In Part I it is shown how, from the integral of the general differential equation of the electric circuit, which has been discussed in a previous paper, all the types of electric currents are derived as special cases, corresponding to particular values of the integration constants. The equations of the circuits with massed constants, that is, the usual electric circuits, are derived by substituting zero for the (electrical) length of the circuit. Besides the general transients, discussed in a previous paper, three main classes of currents are shown to exist, corresponding to different values of the time exponent b: The alternating currents, corresponding to b = imaginary, which are the useful currents of our electric circuits. The impulse currents, corresponding to real values of b, which may be called harmful currents of our electric circuits. And, as limit case, for b = 0, the continuous-current circuit with distributed constants. The last case, a continuous current in a circuit with distributed resistance and leakage, is discussed, and it is shown that such continuous-current circuit has many features which are usually considered as typical of alternating-current wave transmission. It consists of a main current and a return current; complete reflection occurs at the end of the circuit; partial reflection at a transition point; a surge resistance exists, which, connected to the circuit, passes the current without reflection. In Part II an outline of the theory of impulse currents is given. They comprise two classes, the non-periodic and the periodic impulse currents. The equations of both are given in different form, by exponential and by hyperbolic or trigonometric functions. Their characteristics are: Impulse current and voltage may be resolved into a main wave and a return wave. The return wave is displaced from the main wave in time and in position. A time displacement exists between the two current waves and their corresponding voltage waves. This time displacement may be a lag of the current behind the voltage, or a lead, depending on the circuit constants. In the periodic impulse currents, the displacement between main wave and return wave is represented by a position angle, and the two current waves are in quadrature in position, to their respective voltage waves. A few special cases are discussed.