INDUCTANCES AND RESISTANCES 

 of output E (Figure 4.11), the response is of the exponential type, for we have 



If the instantaneous current is /, then F^ = iR, and F^ = —e, that is, 



Figure 4.11 

 minus the back e.m.f. across the inductance, which is -\-L dijdt. 



E=iR + L dijdt 



for which the solution is 



K 



Thus the current rises from at r = 0, to a final value EjR with a time 

 constant LIR. Since LjR is the time / would take to reach EjR if the imtial 

 rate of current rise were maintained, it follows that the inhial rate of current 

 rise is EjL, which is the same as the case for which the resistance is not 

 present. The effect of R is to prevent the current rising steadily towards 

 infinity, limiting it to the value EjR. 



Self inductance and resistance in series, connected to a constant-voltage 

 alternator 



If R and L are connected to a generator of vector output V {Figure 4.12), 

 the current which flows round the circuit is Vl{R -\- jX£) and the potential 



v/(R^jXl) 



© 



(^, 



R 



R 



.l^m 



''out 



Figure 4.12 



Figure 4.13 



difference it produces across R is (VR)I(R + jXj) and across C is (jVX^)! 

 (R + jXj). These expressions could be the basis for another whole series of 

 filters, for in the arrangement of Figure 4.13 we have 



out 



J^I 



1 



Fin R+JXl 



1 + 



R_ 

 59 



out 



in 



1 



'A 



2 U/2 



+ 1 



