The Resistance of the Spark and Its Effect on the Oscillations of Electrical Oscillators

The author shows that the Kelvin theory of oscillating circuits (the logarithmic decrement theory) is applicable only when the spark resistance is small, and not when it is predominant in the circuit. In homologous circuits at audio and radio frequencies, the condenser potential difference will be much higher in the radio frequency circuit, and spark phenomena will control the law of current amplitude decrease. Braun tube oscillograms of radio frequency circuits with predominant spark resistance show a linear and not logarithmic decay of the current amplitude. For circuits having a linear decrement, the values of current and circuit resistance at the end of any time are derived. The new expressions, which are simple, are compared with those of the logarithmic decrement theory. The summational current effect for a number of wave trains, in the case of circuits having a linear decrement, is obtained and discussed. In studying leakage in condensers, it is shown that the effect of dielectric hysteresis in condensers is equivalent in effect to either a conductance in parallel with the condenser or a resistance in series with it. A new feature, namely the difference in the capacity value of the condenser in the two cases mentioned, is considered.