EFFECTS OF CAPACITY. 29 



which shows that the current is in advance of the 

 P.D. by a time given by 



that is, by a quarter of a period. 



Thus, by reference to 21, Chap. III., we see that whereas 

 self-induction causes the current to lag behind the applied P.D., 

 capacity causes the current to lead before the P.D., and whereas 

 E.M.F. of self-induction lags a quarter of a period behind the 

 current, the E.M.F. due to capacity leads a quarter of a period 

 before the current. The E.M.F.s due to self-induction and capacity 

 in the same circuit are thus seen to be in direct opposition, and 

 may, under suitable conditions, completely neutralize one another. 



We will now proceed to calculate the value of the current in 

 alternating current circuits containing capacity. 



23. Electric Current in a Circuit containing? 

 Resistance and Capacity only. Consider a circuit of 

 total resistance r containing a condenser of capacity C. Let an 

 alternating E.M.F. e = fisin pt be applied between the ends of 

 the circuit, and let i be the resulting current. 



The function of e is to drive the current i against the resistance 



r of the circuit, and to balance the E.M.F. ^ due to capacity, where 



Q is the charge on the condenser at any instant. We, therefore, 

 arrive at the equation 



ri + = 8mpt ....... (4) 



L> 



Differentiating this with respect to t, we get 

 di , IdQ 



or 



di , i 



r-j- -\--fr =pE cospt W 



ctt L> 



The complete solution of this equation is (see Appendix) 



M? + *-* .... (6) 



