Abstract :
The oscillating-current circuit differs from the alternating-current circuit in that the sinusoids involved are damped. In the same way that alternating-current theorems are obtained by generalizing direct-current theorems, it is possible to obtain oscillating-current theorems by still further generalization. This involves a generalized angular velocity and a generalized impedance which are complex quantities. Kirchoff´s law may be thus generalized; and yields a simple method of determining the generalized angular velocities, and thus the frequencies and decrements, of free oscillation. Since, in an oscillating-current circuit, there is no impressed voltage, the initial voltage present in the circuit must be used in determining the amplitudes of oscillation. This results in the introduction of a “threshold impedance” for use in determining the amplitudes, which is obtained by a single differentiation from the generalized impedance. Further direct-current rules may also be readily generalized for convenient use in the solution of oscillating-current circuits. A simple example is given to show the method of procedure. The discharge of a leaky condenser through a reactor furnishes a second example which better illustrates the convenience of the method for numerical computations. As a third example the oscillation of a three section artificial cable under particular terminal conditions is chosen. The algebraical portion of this example is given in an appendix. A list of symbols used will be found at the end of the paper.
