62 TREATISE ON ALTERNATING CURRENTS. 



Reactance. We shall denote the quantity pL - ~ by 



the letter s, and call it the reactance of the circuit. 

 Equation (9) then becomes 



ri + Jcyi = c ....... (10) 



If the P.I), is given at any instant by 



E sin lit 



the corresponding current is given by 



E sin (pt - 0) 



From equation (10) we get 





Equations (10) and (11) are equations (1) and (3) extended to 

 the case in which the circuit contains both self-induction and 

 capacity, the former being an equation of E.M.F.s, and the latter 

 an equation of currents. 



The magnitude of c is given by 



c = Vr 2 -f * a . i 

 whence 



e 



and the impedance of the circuit is 



V'r* 4- s 2 (12) 



SERIES CIRCUITS. 



46. Suppose that m reactive circuits are connected in series, 

 and that an alternating P.D. c is applied between the extreme 

 terminals of the combination. We propose to determine the 

 equivalent resistance E, and the equivalent reactance S, of the 

 combination. 



