A Treatise On the Theory of Alternating Currents 2

Alexander Russell

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. + -4n sin (na)t — n)y and €p = A isia {(ot — i — (p — 1) a] +,..+ An sin [neot - <^n - ^ (i> — 1) a}. Therefore, since e = ^1 -f ^2 + . . . -f 6|p, we have . pna + An — sin (ruot - <^„ -^^^ naj . srny Hence if sin ^-^ / sin -^ is less than sin -^ / sin ^ the ratio of the amplitude of the nth to that of the first harmonic is less in the resultant wave than in the wave generated in a single coil. We see also that if 8m(pna/2) is zero and sin(7ia/2) is not zero, the nth harmonic in the resultant wave vanishes. In a single in] INCLINED POLE PIECE 127 phase machine pa is tt, and as n is always an odd number in practice the nth harmonic is not annulled. Consider now the case of a three phase machine with a rotating •armature. In this case we have pa equal to 27r/3, hence pwa/2 = utt/S, and 7ia/2 = W7r/3p. If w be a multiple of 3 but not of Sp, there is no nth harmonic in the resultant electromotive force wave. The variation of the reluctance of the magnetic circuit due to the slots in the armature can be prevented by two methods.

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