58 TREATISE ON ALTERNATING CURRENTS. 



and the impedance / is given by 



44. To find the Current passing through a 

 Circuit containing a Resistance of r Ohms in 

 Series with a Capacity of C Farads, when an 

 Alternating P.D. of e R.M.S. Volts having Fre- 

 quency n is applied between its Terminals. 



Let > = 2?r?i 



and i = the R.M.S. current in amperes. 



The E.M.F. necessary to drive the current against the resist- 

 ance of the circuit is 



ri 



The E.M.F. due to capacity is 



Jci 

 pG 



by 38 and 40, since it leads a right angle before the current ; 

 therefore the E.M.F. required to balance it is 



ft 



P C 



The applied P.D. has therefore to be capable of resolution into 

 the two components, ri and --- ~; thus we arrive at the vector 

 equation 



This equation is represented graphically in Fig. 19, in which 

 OP is the vector ri, OQ' the vector representing the E.M.F. due 

 to capacity, PQ the vector representing the E.M.F. necessary to 

 balance that due to capacity, and OQ that representing the applied 

 potential difference. 



The magnitude of e is, by 35, given by 



= \/ r 2 + -oTw i 



therefore 



