506 M. I. Pupin — Electrical Oscillations of 



as ordinates are given in Fig. 1. The current curves are given 

 in Fig. 2. (I am very sorry that these diagrams have come 

 out very indistinct in the reproduction.) 



With small resistance in the secondary the efficiency is high 

 but the output is very low, and vice versa, when the resistance 

 in the secondary is large then the primary current is large but 

 the efficiency is low. 



With ordinary transformers we have just the opposite re- 

 lations, namely, the lower the resistance in the secondary the 

 larger is the current in the primary. Here, however, owing to 

 the fact that the counter electromotive force in the primary 

 produced by the variation of the secondary current differs by 

 half a period in phase from the primary impressed e. m. f., it is 

 evident that the larger the secondary current the smaller is the 

 effective e. m. f. in the primary circuit and hence the smaller 

 is the current. 



Let E c = counter electromotive force in the primary due to 

 variation of the secondary current. 



„, „ ,, dy w s M 2 E 



Then E c = M -f- = £= — =^ sin pt. 



clt p-M'+.BS 



Hence effective e. m. f. in the primary 



= E sin pt — E c 



RSE 



= -^rr» — sb sm Pt- 

 pM- + RS r 



When S = then the primary current would be equal to zero 

 but the secondary would have its highest value 



_E 

 ~ pR' 



These few remarks seem sufficient to clear up the rather sur- 

 prising relations which the curves in fig. 1 illustrate. 



When the frequency is very high, say 10 4 periods per second, 

 then as long as S does not increase beyond the value at which 

 RS is comparable to j9 2 M 2 so long will 



SE . 



sin pt . . . . 



p 3 W 



y = jm cos pt 



T>' T SE 



(100 



Denoting the limiting values of these quantities (for S = oo ) 

 by brackets we shall have 



