Overdamped Condenser Oscillations

In the classical equations of the discharge of a condenser of capacity C into an external circuit of resistance r and inductance L, it is found that the discharge is oscillatory if r ≪ ??4L/C, and is impulsive if r ≫ ??4L/C. As the perfect condenser can never be realized in practise, it is the purpose of this paper to show the effect of the condenser leakage on the discharge wave. The imperfect condenser is represented by the perfect condenser C shunted by the conductance g. This condenser discharges into the circuit L and r as above. The mathematical discussion shows that no matter what the relation between r and ??4L/C, there may always exist some value of g for which the discharge is oscillatory. This is the case when (r/L - g/C) ?? 4/LC i, e., r ≪ ??4L/C+ gL/C It is to be borne in mind that the above holds true only when r, L, C, and g are constant. If the resistance is that of a third class conductor, the discharge will always be oscillatory. An apparent paradox is found in the statement that the current may be more than 90 deg. out of phase with the voltage. A study of the derived equations, remembering that the current under consideration is only one of the two components forming the total discharge current (C de/dt) of the condenser (the leakage current g e being the other), will show that this is true.