126 ELECTRICAL ENGINEERING 



The vector diagram for the circuit is shown in Fig. 96, and the 

 current and e.m.f. waves are shown in Fig. 97. A series circuit 

 in which the inductive reactance and the condensive reactance 

 are equal at a certain frequency is said 

 to be in a state of resonance for that 

 frequency. In commercial circuits the 

 capacity is usually so small that reso- 

 ijance cannot occur at ordinary frequen- 

 c j eg ^ j^ wnen anv hjgh frequency e.m.f. 's 

 E=EI=IR= 200 voit are p rO (i UC ed in the circuit resonance may 



occur and very large e.m.f. 's may appear 

 and break down the insulation. 

 E 3 =ix c =628v<>u B ' (2) If an alternating e.m.f. E = 200 



FIG. 96. Resonant circuit. volts at a frequency / = 60 cycles per 

 second is impressed on the circuit in Fig. 



98, determine the value and phase relation of the main current 

 and the currents in the three branches. 



The first branch is a resistance R = 40 ohms; the second 

 branch is an inductance L = 0.1 henry and has a reactance 

 X = 2irfL = 37.6 ohms at 60 cycles; the third branch is a ca- 

 pacity C = 100 microfarads or 10~ 4 farads and has a reactance 



= 26 - 4 ohms - 



The current in the resistance is 



E 200 

 /l = R = 40 = 



in phase with the impressed e.m.f.; the current in the inductive 

 reactance is 



T E 20 KO 



Iz = j = oy-g 5-3 amperes, 



90 degrees behind the impressed e.m.f.; the current in the con- 

 densive reactance is 



E 200 _ 



90 degrees ahead of the impressed e.m.f. 

 The main current is 

 I = V/! 2 + (/, - 7 3 ) 2 = V5 2 + (5.3 - 7.6) 2 = 5.5 amperes, 



