KENNELLY. — OSCILLATING-CURRENT CIRCUITS. 377 



The admittance of the oscillating-current circuit is given by the 1" 

 vector, Figure 3, which is drawn in the —j direction to a scale of mhos, 

 and a length of cw mhos. In the case considered Y = —^'0.006,324,6 

 mho. 



The initial vector oscillating current is given by the /vector, Figure 3, 

 which is drawn in the —j direction to a scale of amperes, and a length 

 of Uq Y, as the amplitude, or maximum cyclic value, of the p. d. at 

 condenser terminals. Or, expressed in terms of the quantity of elec- 

 tricity in the condenser, Iq = Qqm, where ^o is the initial condenser 

 charge in coulombs, and the vector amplitude or maximum cyclic 

 quantity. Q^ is also QV^, where Q is the root-mean-square of the 

 oscillating condenser charge, in coulombs. In the case considered, 

 /o is —J 6.3246 amperes, and 7 = 4.472,14 r. m. s. amperes. This 

 shows that in Figure 2 the current vector OIo — 6.3246 max. cyclic 

 amperes, lies 90° in phase behind the discharging p. d. Olio- 



The oscillatory power in the circuit is given by the F vector. Figure 3. 

 Since the current is in quadrature with the emfs. in a resistanceless 

 circuit, the power will be wholly reactive or non-dissipative. The P^ 

 vector is drawn in the —J direction, to a scale of watts, and to a 



length of Pot = —^ = U^^ units on this scale. In the case considered 



P^ — —J3 162.3 watts. This is the maximum cyclic value, or ampli- 

 tude, of the power of the condenser. The power is positive when the 

 condenser is doing work, or discharging, and is negative when the 

 condenser is receiving energy from the magnetic field of the coil, or is 

 charging. 



The oscillatory energy in the circuit is given by the W vector. 

 This vector is drawn in the = —J direction, to a scale of joules, and to 

 a length of W^ = P/2id units on that scale. In the case considered, 

 Wfn = —jl joule. This is the maximum cyclic value, or amplitude, 

 of the energy delivered by the condenser into the magnetic field of the 

 coil at each oscillation. 



The time variation of the various oscillating quantities is represented 

 in Figure 5, for one complete cycle of the current and p. d. The sinu- 

 soid u, n, u, of 1000 volts amplitude, is the graph of the condenser 

 p. d., commencing at Uo = 1000 volts. The sinusoid e is the emf of 

 self-induction in the coil, and is always equal and opposite to the 

 p. d. of the condenser. The sinusoid il, of 6.3246 amperes ampHtude, 

 is the graph of the discharging current, and is 90° in phase behind the 

 discharging p.d. The sinusoid/*, of double fi-equency, and of amplitude 



