70 TKEATISE ON ALTERNATING CURRENTS. 



Capacity, are placed in Series between Alter- 

 nating-current Mains : find the Fall of Potential 

 along 1 the Inductive and Capacity Parts re- 

 spectively. 



Let XY (Fig. 22) be the circuit containing resistance r\ and 



FIG. 22. 



self-induction L, and YZ that containing resistance r 2 and 

 capacity C. 



Let the E.M.S. value of the P.D. between X and Z be V\ that 

 between X and Y y v\ ; and that between Y and Z, r 2 . 



Let i be the K.M.S. current flowing along XYZ. 



Put 



and 



~ 



2irnC 



so that si and s 2 are the reactances of JTF and Y% respectively, and 

 n is the frequency of the current. 



Then we have (see 43), since it is a series arrangement 



whence the magnitudes of V t vi, and v* are respectively given 

 by- 



v = 



therefore 

 Vl : v 2 : V= \/ri 

 To more fully illustrate this case, suppose that 



n = 100 



L = 5 henrys 



TI = 5 ohms 



r. 2 = 10 ohms 



C = 0'5 microfarad 



