. Theory and calculation of alternating current phenomena . l cases. Hence the general alternating-current wave is expressed by: i = 7] sin 2 Trf(t — ti) + 13 sin 6 Trf(t — ts)-\- hsin lOirfit -U) -{- . .or, i = A\ sin 2Tvft + A3 sin 6x/f + ^5 sin lOvr/^ + . . + Ex cos 2 irjt + Bz cos 6 irft + B5 COS 10 tt/^ + . . I I I I I I I I I I I ) i Fig. 2.—Wave without even harmonics. Such a wave is shown in Fig. 2, while Fig. 3 shows a wavewhose half-waves are different. Figs. 2 and 3 represent the sec-ondary currents of a Ruhmkorff coil, whose secondary coil isclosed by a high external resistance; Fi
. Theory and calculation of alternating current phenomena . l cases. Hence the general alternating-current wave is expressed by: i = 7] sin 2 Trf(t — ti) + 13 sin 6 Trf(t — ts)-\- hsin lOirfit -U) -{- . .or, i = A\ sin 2Tvft + A3 sin 6x/f + ^5 sin lOvr/^ + . . + Ex cos 2 irjt + Bz cos 6 irft + B5 COS 10 tt/^ + . . I I I I I I I I I I I ) i Fig. 2.—Wave without even harmonics. Such a wave is shown in Fig. 2, while Fig. 3 shows a wavewhose half-waves are different. Figs. 2 and 3 represent the sec-ondary currents of a Ruhmkorff coil, whose secondary coil isclosed by a high external resistance; Fig. 3 is the coil operatedin the usual way, by make and break of the primary battery 8 ALTERNATING-CURRENT PHENOMENA current; Fig. 2 is the coil fed with reversed currents by a com-mutator from a battery, 7. Inductive reactance, or electromagnetic momentum, whichis always present in alternating-current circuits—to a large ex-tent in generators, transformers, etc.—tends to suppress thehigher harmonics of a complex harmonic wave more than the. Fig. 3.—Wave with even harmonics. fundamental harmonic, since the inductive reactance is pro-portional to the frequency, and is thus greater with the higherharmonics, and thereby causes a general tendency toward simplesine shape, which has the effect that, in general, the alternatingcurrents in our light and power circuits are sufficiently near sinewaves to make the assumption of sine shape permissible. Hence, in the calculation of alternating-current phenomena,we can safely assume the alternating wave as a sine wave, with-out making any serious error; and it will be sufficient to keep thedistortion from sine shape in mind as a possible disturbing factor,which, however, is in practice generally negligible—except in thecase of low-resistance circuits containing large inductive reactanceand large condensive reactance in series with each other, so as toproduce resonance effects of these higher harmonics, and alsounder certain cond
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