INDUCTANCES, CAPACITANCES AND RESISTANCES 



We have Z, = R +jl(oL - ^j 



1 //. 

 R 



Let 



Q\c) 





then, letting 



^0 — /'A/-\l/2 



(^C)i 



7 — — 

 "^^ coC 



a> 



Mr. 



'«! 



Q 



WJ 



CO 



1 f 1 /a> 



co„ 



CO 



;)1 



_j_/i_+(i^_^A'r' 



CO 



oC\Q' 



.CO. 



CO 



\jo}^C is a constant for the circuit. In Graph 24, the impedance of a 

 series resonant circuit is plotted in the form \Z^ oi^C as a function of frequency 

 for various Q. 



Parallel L-C-R circuit connected to constant-current generator 



The parallel circuit of Figure 5.5 is of importance because, if a capacitance 

 be connected across a real inductor, then the real inductor is represented by 

 an ideal inductance L in series with the resistance of the wire comprising the 



\ 



Open at 

 6 f = 



(§ / 4 



Lighrtly damped 



r=0 



Figure 5.5 



Figure 5.6 



inductor, R. If this circuit be suddenly fed with a current /, it settles down to 

 a final state in which all of / flows through L and R by one of three ap- 

 proaches — oscillatory, critically damped, or heavily damped {Figure 5.6) in a 

 manner analogous to the capacitance voltage when series L-C-R is connected 

 to a constant-voltage generator. As in the series case, critical damping occurs 

 at R^jAD = 1/LC. 



77 



