104 



ELECTRICAL ENGINEERING 



If an alternating current i = 7 sin = 7 sin 2 irft is flowing 

 through a circuit of inductance L henrys and negligible resist- 

 ance an e.m.f. of inductance will be set up 



T di 

 eb= - L dt 



-r d , 



(148) 



= 27r/ZJ sin(27r/Z- 90); 



it is a sine wave of e.m.f. lagging behind the current wave by 

 90 degrees. (Fig. 75.) 



FIG. 75. Inductance in alternating current circuits. 



In order to drive the current through the circuit an e.m.f. 

 must be applied to the terminals, which at every instant will be 

 equal and opposite to the back e.m.f. e&; its instantaneous value 

 is 



e = - e b = 2 TT/L/O sin (2 vfl + 90), . . . (149) 



a sine wave of e.m.f. leading the current wave by 90 degrees. 

 This e.m.f. is consumed by the inductance of the circuit. 

 maximum value is 



E = 27r/L7o, ....... (150) 



Its 



where the term 27T/L is called the inductive reactance of the 

 circuit and is denoted by X. It is of the nature of resistance and 

 is expressed in ohms. 



