Distortion of Alternating-Current Wave Caused by Cyclic Variation in Resistance

An alternating current flowing through an unvarying non-inductive resistance has a wave-form that is undistorted and is identical with the wave-form of electromotive force. If the resistance varies during each cycle, on account of changing current and temperature or other causes, the current wave-form will be distorted and will contain a third harmonic that will flatten the current wave when the temperature coefficient is positive and will peak the current wave when the temperature coefficient is negative. If there is no temperature lag in the resistance (that is, if the maxima and minima of temperature and resistance coincide with the maxima and minima of current), the maximum of the third harmonic in the current wave will coincide with the maximum of the fundamental, so as to flatten or peak the wave as stated. A temperature lag in the resistance, however, causes the third harmonic of the current to be retarded in phase, and likewise causes a slight shifting of the fundamental of current with respect to the electromotive force. Due to this distortion of current wave-form, power factor becomes less than unity and a vector diagram in more than two dimensions is required to show the true relations between current, electromotive force and power factor. These conclusions, reached theoretically, conform with the experimental facts so far as known. In practical cases cyclic change of resistance is so small that the distortion due to it is insignificant.