186 THE MAGNETIC CIRCUIT [ART. 58 



calculated for some important practical cases, from the forms and 

 the dimensions of the magnetic circuits, using the fundamental 

 equations (104), (105) and (106). The reader will see that the 

 problem is reduced to the determination of various permeances and 

 fluxes; hence, it presents the same difficulties with which he is 

 already familiar from the study of Chapters V and VI. 



Inductance of electric circuits in the presence of iron. When 

 iron is present in the magnetic circuit, three cases may be distin- 

 guished : 



(1) The reluctance of the iron parts is negligible as compared 

 to that of the rest of the circuit ; 



(2) The reluctance of the iron parts is constant within the 

 range of the flux densities used ; 



(3) The reluctance of the iron parts is considerable, and is 

 variable. 



In the first two cases, eqs. (104), (105) and (106) hold true, and 

 the inductance can be calculated from the constant permeances of 

 the magnetic circuit. In the third case, inductance, if used at all, 

 must be separately defined, because eq. (1026) does not hold when 

 the permeance of the circuit varies with the current. The equa- 

 tion of energy is in this case 



W=n 



f niMUttf). . . (108) 

 Jo 



This equation is deduced by the same reasoning as eq. (98) . 



The following three definitions of inductance are used by differ- 

 ent authors when the reluctance of a magnetic circuit is variable: 

 (a) the expressions (104) and (108) are equated to each other, and 

 L is calculated separately for each final value i of the current. 

 Thus L is variable, and neither eq. (105) nor (107) hold true. (6) 

 L is defined from eq. (107) ; in this case neither eq. (104) nor (105) 

 are fulfilled, (c) L is defined at a given current by eq. (105) so 

 that Li represents the sum of the linkages of the flux and the cur- 

 rent. Therefore eq. (107) becomes e = -d(Li)/dt, and dW =id(Li) . 

 With each of the three definitions L is variable, and therefore is not 

 very useful in applications. The author's opinion is that when the 

 permeance of the circuit is variable, L should not be introduced at 

 all, but the original equation of energy (108) be used directly. Or 

 else in approximate calculations, a constant value of L can be 

 used, calculated for some average value of i or $. 



