VECTOR-DIAGRAMS OF OSCILLATING-CURRENT CIRCUITS. 

 By a. E. Kennelly. 



Presented November 9, 1910. Received November 25, 1910. 



Although, as the appended bibliography indicates, the analysis of 

 oscillating-current circuit phenomena has received much attention, and 

 has attained a considerable degree of development, yet the methods of 

 vector- diagrams do not seem to have been applied to it. It is believed 

 that these vector-diagram methods offer marked advantages to the 

 student, and particularly to students of electrical engineering who have 

 already become familiar with the use of vector-diagrams in connection 

 with alternating-current circuits. 



Definition. 



An oscillating-current circuit may be defined as a circuit which, in 

 undergoing a change of energy, carries a current that oscillates peri- 

 odically about an ultimate value. In such a circuit not only the electric 

 current, but also the emf quantity, power, and energy oscillate freely. 

 For brevity, the term oscillating current may be designated by the 

 letters o. c. In practice, an o. c. circuit comprises a condenser as an 

 essential element, the energy oscillating, or tending to oscillate, be- 

 tween the electric and magnetic types, at a frequency determined solely 

 by the constants of the circuit. The oscillations decay in amplitude, 

 energy being expelled irrecoverably from the circuit, during the process, 

 by a regular sequence of dwindling impulses. These impulses may be 

 either of the joulean or hertzian type, or of both combined. 



Simple Resistanceless Oscillating-Current Circuits. 



The simplest type of o. c. circuit comprises a condenser AB, Figure 1, 

 of capacity or permittance c farads, inserted in a circuit of negligible 

 resistance, containing a total inductance of / henrys. Let n be the free- 

 oscillation frequency of the circuit, in cycles per second, and let w = ^irn 

 be the free-oscillation angular velocity of the circuit, in radians per 

 second. Then the reactanceJXj of the inductance DEbX this frequency 

 will be 



jXi=jloi ohms (1) 



