CAPACITY REACTANCE u 



othrr, and we see that in the case considered the impressed e.m.f. and 

 the current are in quadrature with each other. Further, again con- 

 sidering r.m.s. values, we see that 



, e.m.f. 

 current = - 



pL 



Tl 10 quantity pL is termed the reactance of the circuit. 



Consider a condenser of capacity C, across whose terminals there 

 is an impressed p.d. given by 



v ss V sin pt 

 Let q = instantaneous quantity or charge in the condenser. Then 



q = Cv = CV sin pt 

 If i as instantaneous current, then clearly i = J*, or 



CLL 



i = pCV cos pt 

 In a vector diagram, therefore, the current would be represented 



by a vector which is or 90 ahead of the 

 z 



p.d. vector, as in Fig. 7. The p.d. and 

 current are in quadrature with each other, 

 and the p.d. lags behind the current. 



The r.m.s. values of the p.d. and cur- 

 rent are connected by the relation 



current = p.d. X Cp = *-^ 

 C^ 



and --;- is spoken of as the reactance of the FIG. 7. Vector Diagram for 



^P Pure Capacity, 



condenser. 



Let the resistance of a circuit be r, and its self-inductance L. In 

 order to maintain a current 



i = I sin pt 



in the circuit, we must, by equation (1), provide an impressed e.m.f. 

 of amount 



= rl sin pt + pLI cos 2>t 



The first component of the impressed e.m.f., viz. rl sin pt, may 

 be represented, in a vector diagram, by the projection of a rotating 



