406 Prof. G. M. Minchin's Graphic Representation 



frequency employed ; but, as is seen from the previous theo- 

 retical investigation, by employing a primary and a secondary 

 having equal time-constants suitably related to the frequency, 

 and a pure sine function P.D., an increase of impedance of 

 from 10 to 12 per cent, ought to be obtained; 15J per cent, 

 increase could never be obtained in practice, as there must- 

 always be some magnetic leakage. 



In transformers with iron cores this effect would never be 



likely to escape notice as the values of =~ would be so large 



that the critical frequency would be very small, so that for all 

 frequencies employed in practice the impedance of the primary 

 would diminish on closing the secondary. The iron core 

 would also distort the current from a pure sine function. 



XXXVI. Graphic Representation of Currents in a Primary 

 and a Secondary Coil. By Prof. G. M. Minchin, M.A* 



IN this short paper is contained a solution of the following 

 problem : — A primary and a secondary coil occupy given 

 positions ; an alternating E.M.F. , expressed by a sine function 

 of the time, being applied to the primary , it is required to 

 represent graphically the impedances and phases of the primary 

 and secondary currents for all speeds of alternation. (No iron 

 cores employed.) 



The occasion of this communication was a paper read 

 to the Physical Society on the 27th of October, 1893, 

 by Mr. Rimington, in which the subject was presented in a 

 different manner. 



Adopting the notation of Mr. Rimington's paper, let L, M, 

 N, r ly r 2 be, respectively, the coefficient of self-induction of 

 the primary coil, the coefficient of mutual induction, that of 

 self-induction of the secondary, and the resistances of the 

 primary and secondary. Also let n be the frequency of the 

 alternation, i. e. the number of alternations per second ; 

 p = 2irn\ E = maximum value of the impressed E.M.F. 

 Then, if the secondary coil is open (or r 2 = <x> ), the impedance, 

 I, of the primary is given by the expression 



i 1= ^+Ly. 



The impedance, I 2 , of the secondary, if the primary were 

 absent and the secondary plied by an alternating E.M.F. , 



* Communicated by the Author. 



