KENNELLY. — OSCILLATING-CURRENT CIRCUITS. 375 



oscillation such that the reactance of the circuit remains zero. This is 

 the law of all oscillating-current circuits, whether they contain small or 

 large resistance, up to the aperiodic limit. Consequently : 



jA^i—jXc = ohms (3) 



jlui =j— =j - ohms (4) 



whence 



0, = -L= = i/-. radians/sec. (5) 



Vic I 



When condensers are connected in parallel, their permittances 

 are more readily dealt with ; and when connected in series, their 

 elastances. 



Dhcharging Oscillations of a Simple Resistanceless Oscillating- 

 Current Circuit. — The oscillatory system of Figure 1 may be given 

 its initial stock of energy either electrically or magnetically ; that is, 

 either by giving an initial electric charge of Qo coulombs to the con- 

 denser, or by exciting a total initial linked magnetic flux $o = lol 

 ampere-henrys in the coil, where /q is the initial exciting current- 

 strength, supposed to be suddenly withdrawn from the coil without 

 loss of energy in sparking. With respect to amplitude, the discharging 

 oscillations of the coil will be the same as those of the condenser, pro- 

 vided that : 



*^o = ^0-0 volt-seconds (6) 



where ~o = r " = V*^^ is the surge impedance of the system. With 



respect to phase, however, the discharging oscillations of the excited 

 coil will be in quadrature with those of the excited condenser. In 

 cases where both the condenser and the coil are initially excited, and 

 are allowed to discharge simultaneously, each may be considered inde- 

 pendently, and the two sets of oscillations may then be summed. 



General Rotating Vector -Diagram of Shnple Resistanceless Oscillat- 

 ing -Current Discharging Circuit. — In Figure 2, let OUo represent to 

 volt-scale the initial p. d. applied to the condenser of Figure 1, and 

 producing therein an initial electric charge Qo. Then Uq will be the 

 equal and opposite p. d. of U^ volts, tending to discharge the condenser. 

 The direction of the discharging p. d. OU^ may be taken as the direc- 

 tion of reference or voltage phase-standard, and XOX as the axis of 

 reference. The vector 01^ then represents the discharging current 

 established by the discharging p. d. OU^. The vector system OUo, 

 OIq, OEq is to be pivoted about the point 0, and, starting at time 



