EFFECT OF CAPACITY. 121 



The total voltage of the circuit __ 



= V(energy voltage)* + (idle voltage) 2 . 

 Suppose the energy voltage to be due to 10 amperes 

 flowing through '5 ohm, its value will be 



10 x -5 == 5 volts. 

 Let the inductance idle voltage == 2 TT n L c = 



C 

 200 volts, and the capacity idle voltage == ^ ^ 



~160 volts, the negative sign indicating that the phase 

 of the capacity idle vbltage is opposite to that of the 

 inductance idle voltage. 



The total idle voltage of the circuit is 

 then = 200 - 160 = 40 volts. _ 



The total voltage of the circuit = = /v/5 2 + 40 2 = 

 V25 + 160=\/185= 13'6 volts, whereas the voltage in 

 the inductance is 200, and across the condenser is 160. 



Cases of this kind frequently occur in practice in con- 

 nection with long concentric mains which have considerable 

 capacity. The self-induction of the generator armature, 

 of the cable itself, or of machines connected to the cable, 

 may supply the inductance in the circuit. 



In the ideal case where no losses occur in the circuit 



s> 



due to resistance, &c. , if 2 -a- n L c = -- ^ the voltage of the 



- 



condenser and choking coil will be exactly equal and 

 opposite. Consequently, a very small voltage applied to 

 the circuit might theoretically give rise to an indefinitely 

 high voltage in each portion. The action is due to the 

 periodicity of the current being exactly so timed in this 

 case as to correspond with the natural period of charge 

 and discharge of the condenser under the conditions 

 existing in the circuit. ' A repetition of a small periodic 

 electromotive force of this periodicity is thus sufficient to 

 produce very large currents and consequently high 

 voltages at. the terminals of the condenser. 



The expressions given above enable a determination 

 to be made of the conditions under which resonance can- 

 occur, and the extent to which it will exist in each portion 

 of the circuit. 



Capacity and Inductance in Parallel. In the previous para- 

 graph it was found that the effect of a capacity and self- 

 induction connected in series was that the idle electro- 



