ELECTRIC CIRCUITS 87 



64. Inductance. When a current of electricity flows in a 

 circuit, lines of magnetic induction interlink with the circuit; if 

 the current remains constant the flux threading the circuit is 

 constant, but when the current varies the flux varies propor- 

 tionally and in doing so generates in the circuit an e.m.f. pro- 

 portional to the rate of change of the interlinkages of flux and 

 turns or to the product of the turns and the rate of change of the 

 flux. This e.m.f. has a value 



e = ft -^ c.g.s. units, . . . . . (121) 



where n is the number of turns in the circuit and - is the rate 



at 



of change of the flux interlinking with the turns. The negative 

 sign is used because the e.m.f. produced opposes the change in 

 the current and, therefore, the change in the flux. 



The number of interlinkages of flux and turns for unit current 

 in the circuit is called the inductance of the circuit and is repre- 

 sented by X, thus, 



X = ^c.g.s. units, ..... (122) 



where i is the current in c.g.s. units, 



< is the flux produced by current i, 

 n<j) is the number of interlinkages for current i.- 

 Equation 122 may be written, 



ruj) = i; 

 differentiating this gives 



and therefore the e.m.f. generated in the circuit due to its in- 

 ductance is 



e=- n ^=-X^ c.g.s. units. . . . (123) 



It is equal to the product of the inductance of the circuit and the 

 rate of change of the current. When e is expressed in volts and 

 i in amperes the inductance is in henrys and is represented by L 

 to distinguish it from the inductance X expressed in c.g.s. units. 

 Equation 123 may then be written 



e=-L~ t volts ....... (124) 



; Y OF ELECTRICAL LABORATORY, 



FACULTY OF APPLIED SCIENCE. 





