ALTERNATING-CURRENT < IRCUITS 43 



mple. A i of 12 ohms, an inductance of 0.2 hrnry and a 



condenser are connected in parallel across 120-volt, 60-cycle mains. For 

 what value of capacitance will the circuit be in resonance? 

 Ic must be equal to IL 



Ic = 120 X 2*r60 X C = 1.59 amp. 



C = 



= 35.2 mf. Ans. 



In the parallel circuit, as well as in the series circuit, LCo> 2 = 

 1.0 at resonance (w = 2irf), when the inductive and capadtive 

 branches contain only pure inductance and pure capacitance. 



Also, under these conditions f - 



2irVLC 



When there is resistance in either the inductive or the con- 

 d< -nsive branch, L and C are the equivalent inductance and capaci- 

 tance of the parallel circuit, and not the L and C, respectively, 

 of the inductance and capacitance alone. 



23. Polygon of Voltages ; Three Voltages. The inductances 

 and condensers so far considered have been assumed as perfect, 

 that is, as having no losses and with their currents exactly 90 

 from their respective voltages. In practice this is impossible. 

 Tin- wire of which the inductance is made has a certain resistance, 

 and if an iron core is used, the core losses are equivalent to an 

 added n-sistance, since they involve a power loss. Condensers 

 are made having very small losses, and phase angles very nearly 

 equal to 1)0, but even such condensers are not ideal. 



When an inductance coil is being considered, its resistance 

 MUM In- added to the other n-MMances in the circuit, in order to 

 find the total cir -uit resiftanoe. 



ire 11 '/) shows a series circuit connected across an alter- 



nating voltage A', having a frequency/. 'This circuit contains a 



/,' and an impedance coil /', having a resistance' A" 



and an inductance /.. The reactance X' of the impedance coil 



i- equal gun 11 (b) shows the vector diagram for 



Circuit, Tin- volt. -me //.' i- in phase with the current /. 



The voltaue /;/ ; , j m ,., | ;i Mn . ,.,,J1 j, ,,, <MI ahea<l of tin* 



current, but lead- the current by an an n 90, 



hie to tli nee of the impedance ooiL The circuit voltage 



