28 ALTBRNA Ti\<; cr/tlil<:\rx 



(In practice it is impossible to obtain a pure inductance, as 

 inductance must necessarily be accompanied by a certain amount 

 of resistance.) 



The above may also be proved as follows: Let the current be 

 given by i = I maf sin wt. The emf. of self-induction 



T di 



e' = L -T = Lul max cos wt . ^ 



at s^^ 



= Lul max sin (<at - 90) 

 is a sine wave lagging 90 with respect to I max sin ut. 



The equation of the line voltage which balances this emf., 



e = Lwl max sin (ut + 90) 

 is a sine wave leading the current I max sin ut by 90. 



The choking effect of inductance is obviously proportional to 

 the frequency and to the inductance. To express this choking 

 effect in ohms, the self -inductance in henries must be multiplied 

 by co = 2irf = 6.28f, where / is the circuit frequency. 



no v 



FIG. 26. Circuit containing FIG. 27. Vector diagram for circuit 



inductance only. containing inductance only. 



That is, 27T/L is the resistance to the flow of current offered by 

 inductance and is called the inductive reactance of the circuit. 

 It is denoted by X L , and is expressed in ohms. 



The current in a circuit having inductive reactance only is 



7 = E/2irfL = E/X L (8) 



The impressed voltage is 



E = 27T/L7 = IX L (9) 



Example. Figure 26 shows a pure inductance of 0.2 henry connected 

 across 110-volt, 60-cycle mains. What current flows? 



X L = 27T 60 X 0.2 = 377 X 0.2 = 75.4 ohms 

 / = 110/75.4 = 1.46 amp. Ana. 



Figure 27 shows a vector diagram for an inductive circuit 

 in which the impressed voltage leads the current by 90. 



