i:s'rTM ATiox AND <'()\'ru()i, OF ()i'i:iv' \ri; timI': ok kklavs 111 



1 Tin; 1 )\ \ \Mi(' lOcjiATioxs 

 '['he notation of this article contni-ins to the list t!;i\('ii on paj^c 257. 



TUl': KLKCTUICAI. IXjlATlON 



'riic \()ltai>;(' ('([ualion for a coil of .V tui-ns linkiiiii a fi(>l(l of sti-en<2;th ^p 

 may he written in the form: 



0- /)A^ + .vt = 0, (1) 



(11 



\vh(M'(> / is \\\v instantaneous current, R is the cii'cuit resistance, and Hi 

 is the constant voltage ap])iied. Writing ;T, for the instantaneous mmf 

 47r A'/, and ;T.s, for the steady state mmf \-k NI, the eciuation Ix'comes: 



(It 



where G, = X' R, the coil constant, or equivalent single turn conduc- 

 tance. If the field ^ is linked by a number of circuits, a similar voltage 

 eciuation applies to each such circuit. By addition of these expressions, 

 there is obtained: 



JF - J.S + 4xG ~ = 0, 

 at 



where t7 = X^' > the total effective mmf, ^s = Yl^si , the total applied 

 mmf, and G ^ ^G; , the total e(|ui\'alent single turn conductance. If 

 the dynamic field has the same pattern as the static field, the instan- 

 taneous mmf 5 must eciual (R<^, where (R is the reluctance 5/V observed in 

 static magnetization measurements. The preceding equation may there- 

 fore be written in the form: 



(R<p - ^s + 47r(; '^ = 0. (2) 



(It 



This relation controls the time rate of development of the flux if. As 

 the coil is the only circuit linking the field that has an externally applied 

 voltage, -Js i.s simply the steady state applied mmf 47r NI. The conduc- 

 tance G includes not only the coil conductance G,- , or N~/ R, but terms 

 for all conductive paths linking the field, including the eddy current 

 paths. The effective conductance of the eddy ciuTent paths is denoted 

 Ge . When a short circuited winding or slee\^e is used, as in slow release 

 relays, its conductance is denoted G'.s . Thus in most cases of interest 

 G = Gr + Ge ; when a sleeve is used, G = Gc -\- Ge -\- Gs ■ 



The static magnetization relations between ^ and (p vary with the 

 position of the armature, which is defined by its displacement x from the 

 operated ])osition. Hence the reluctance i\\ is, in general, a function of 



