PEIRCE. — ESTABLISHMENT OF CURRENT IN COIL. 161 



PART II. SECONDARY CLOSED. 



Theory. — In an iron core built up of varnished sheets of metal 

 there is usually a noticeable amount of magnetic leakage, but in a 

 toroidal core made of one piece of varnished, very fine, soft iron wire, 

 upon which two transformer coils are uniformly and closely wound, 

 the leakage is generally negligible and we may assume with a close ap- 

 proximation to the truth, that if the coils consist of wi and n 2 turns 

 respectively, and if the resistances of their circuits are n and r 2 , the 

 excitation of the core in ampere turns is at any time, 



T = niii + Ttyk 



and if N is the flux of magnetic induction through the core, the corre- 

 sponding fluxes through the two circuits are niN and n 2 N respectively. 

 Let N be determined experimentally at many points of a journey from 

 one magnetic state of the core to another by a given path, and let the 

 results be plotted in the form of a curve, the unknown equation of 

 which may be written in the form N = <& (T 7 ). Let the slope of this 

 curve be obtained at a large number of points so as to give the values 

 of dN/dT or ^f {T) for many values of T, then it is possible to predict 

 the form of a building up curve for a current in the exciting coil which 

 will carry the core over a part, or the whole, of the magnetic path for 

 which we know the values of N as a function of T. 

 The current equations are 



wi dN ■ . . 



El -w'-dT = ri ' ll > (5) 



ih dN . . 



~ 10* ' ~dt = r * ' * (6) 



whence Ein^ = n® • n ■ i\ — rii • r 2 • U, (7) 



wi • r 2 • T -f- W2 2 • E x . 



*i = 9 i 2 » y°) 



■Wi ' T\ ' T — Hi • U2 • Ei 



m 2 • r 2 + w 2 2 • n 



rii dN dT ?n 2 • r 2 • E x — n x • r, • r 2 



10 8 dt dt m 2 • r 2 + rtf • n 



(9) 

 (10) 



10 8 {ni 2 • r 2 • Ei — rii • r x ■ r 2 ■ 1) 



