INDUCTANCES, CAPACITANCES AND RESISTANCES 



The inductance current is VjiR -\- JojL) which, if R is fairly small (Q of 

 circuit high), is approximately equal to —jVjojL. Also, if 7? is small, 

 R <^ {LjCf^ and the resonant frequency is approximately given by co = 

 IJiLCy^ so that coL =^ 1/coC. The capacitance and inductance currents are 



K 



Figure 5.8 



now seen to be equal and in opposite directions; a circulating current flows 

 within the resonant circuit. 



The circulating current is jtoCV = jcoC . liLjCR) 

 The current magnification of the circuit is 



Circulating current 



Generator current 



= jojLlR 



= JQ 



Physically, the circulating current represents the transfer of energy back 

 and forth between electric field in the capacitance and magnetic field around 

 the inductance. At each transfer some energy is lost in the resistance, and 

 this is replaced by a small current from the generator. 



Impedance of parallel resonant circuit when off resonance 



As for the series case, this function is important in the design of tuned 

 amplifiers. We have 



R-\-jojL + ^ 



Let 



JojC 

 j(oL + R 

 jcoCR - o?LC + 1 



-jl-c) 



1 /L\"2 

 Then Z 



oy^LC + 1 



= oiL 



1 



joj{LCfl- + Q{\ - M^LC) 

 79 



