ELECTRIC CIRCUITS 107 



76. Capacity in Alternating-current Circuits. The charge 

 on a condenser or the quantity of electricity stored in it is pro- 

 portional to the difference of potential between its terminals; 

 thus, 



1 = Ce, 

 where q is the charge, 



e is the difference of potential between the terminals, 

 and C is the capacity of the condenser. 



A condenser has a capacity of one farad when one coulomb 

 of electricity stored in it produces a difference of potential of 

 one volt between its terminals. 



If an alternating e.m.f . e = E Q sin 2 Trft is impressed on the 

 terminals of a condenser of capacity C farads, a current i flows. 

 At any time t the charge on the condenser is 



q = Ce, 



but the charge is the amount of electricity which has flowed into 

 the condenser and its value is 



= fV 



Jo 



and therefore 



dt = Ce. 



Differentiating with respect to t gives 



and substituting the value of e, 



= 2TrfCE Q sin (2 irft + 90), . . . . (154) 



and thus the current flowing into the condenser is a sine wave 

 leading the impressed e.m.f. by 90 degrees. Its maximum value 

 is 



(155) 



