50i 3L I. Pupin — Electrical Oscillations of 



electrostatic capacity of the coils is small in comparison to the 

 capacity of the terminal condensers. Foucault currents and 

 hysteresis losses are supposed to be negligibly small. The 

 symbolical expressions of the generalized form of Ohm's law 

 will be, in the well-known notation of Maxwell : — 



L ~ + M % + Rx + P, = E sin pt 1 



H|fM* + *. + P,=-,... j 



Remembering that a circuit consisting of coils whose coeffi- 

 cient of self-induction is L and a condenser of capacity C in 

 series with these coils may be treated analytically like a closed 

 circuit with no capacity but having a coefficient of self-induc- 

 tion equal to -7-^— L,* where p is the pulsation of the im- 

 pressed e. m. f., it is clear that the integrals of (9) are obtained 

 from the well-known integrals of the ideal transformer f by 

 the following substitutions : — 



1 » a M 2 N 



, — o^, — -Li -L JU, — — .,_ T „ — -„ 



1 p 2 Q x 1 p A TS* + i? 



AT l XT 1>> t> i?' 2 M 2 S 



N, = — — - N R = R + J 



yc, rN;+s 2 ' 



When the circuits are in resonance to the impressed e. m. f. 

 then both L r and ~N t are zero. Hence 



SE 



a' = „-.,, — ==r^ sin pt .... 

 pM- + RS 1 



«ME ( 



y = ^mttrs cos pt ■ • • • J 



y 00) 



The corresponding amplitudes of the condenser potential 

 differences are given by 



P -*%TO-- j (n) 



1 p'M' + BJS J 



Let W, = work done in the primary circuit. 

 W a = heat developed in primary circuit. 



* See this Journal, May 1893, p. 425, footnote, 

 f Fleming: Alternate Current Transformer, vol. 1, p. 154. 

 Pupin: Practical Aspects of the Alternating Current Theory, Transactions 

 of the American Institute of Electrical Engineers, Vol. vii, May 1890. 



