INDUCTANCES, CAPACITANCES AND RESISTANCES 



and rises to a maximum EjR when coL = l/o>C, that is, at co = IKLCY'-. The 

 current is then in phase with the apphed vohage and the circuit is said to be 

 'series resonant'. At resonance the vohage across the inductance is given by 



and 



jQ 



(oLjR is the vohage magnification factor of the circuit and in practical 

 cases may be over 100. It is allotted the symbol Q. Since at resonance 

 oi = \l(LCy'-, Q is also given by 



{\l(LCy'}L 



R 



[cR^j 



1/2 



Consider now the voltage across the capacitance. We have, by inspection 



E 



—jlcoC 



^+4™^-^! 



Since Q = {LlCR^f- so that QI^HCR^f'^ = 1 , we have that for the numerator 



Q -jQR 



-jjoiC = —jJcoC . 



{LjCR'-f'^ ~ oi{LCyi^ 



Since Q also equals co^LjR, where w^ is the resonant frequency, QRjcOgL = 1 

 and the denominator can be written 



therefore 



E 



^Y^J o,,l\r ~cocr)j 

 -JQ 



co{LCf'~ i 

 and letting \l{LCf'" = co„ 



1+ye 



O) 



L<^0 



CO . coJLC 



E 



-JQ 



a> 



1 + 



Q 



CO I „i CO 



l + fi^' 



0) 



CO 



211/2 



CO, 



q 



CO I 



This is plotted against co for various Q in Graph 23. Observe how Vq = E 

 at frequencies well below resonance, but that at the resonant frequency the 

 circuit magnifies the generator voltage Q times. Above resonance Vq falls 

 away rapidly. 



75 



