ALTERNATINQ^CURRENT CIRCUITS 



31 



The relations of current and voltage in a condenser circuit may 

 also be proved as follows: 



Let e be the instantaneous voltage across the condenser, C the 

 capacitance in farads, and q the charge in coulombs at any 

 instant. 



Let / = /,, sin ut be the equation of the current. 



-t 



q - J""=/ 7 "" si 



-s 



I m 



sin utdt 

 sin utdt = - 



Ceo 



sin (co< - 90) 



This equation shows that the sine wave of voltage lags the (y 

 urn Tit wave by 90. 

 The average power in a circuit containing capacitance only is zero. 



:n. VoltaRO, current, and pou : circuit containing capacitance 



only. 



This may IK- shown by plotting the power curve from the cur- 



Ige curves, as was done in l ; i^. i>0. This is shown 



the curve of power. There is as much of 



tii'- power curve In-low as atx>V6 the . so tliat the net 



power i- zero, as in a circuit with pun- imluetance only. \Yhen 



.1 to the 

 cirruit and ston-d in lli. ulim the pOW6T GUI 



