RESISTANCE, INDUCTANCE AND CAPACITY 13 



ful lowing three components, represented by the vectors OA, OB, and 

 OC in Fig. 10 : 



(1) The component OA = rl, in phase with the current. 



(2) The component OB = Lpl, SO in advance of the current. 



(3) The component OC = pi, 90 behind the current. 



The lengths of the vectors representing the amplitudes of the 

 components, their projections at any instant correspond to the instan- 

 taneous values of the components, and the algebraical sum of the 

 projections gives the instantaneous value of the impressed e.m.f. 



Now the vectors OB and OC lying in the same straight line and 

 being oppositely directed, the algebraical sum of their projections is 

 equal to the projection of a single vector OD of length equal to 



OB OC = I ( Lp p- J . Finally, the sum of the projections of 



OA and OD is equal to the projection of the single vector OE, which 

 is the diagonal of the rectangle constructed on OA and OD as sides, 

 and which represents the impressed e.m.f. Now 



Hence we see that 



impressed e.m.f. 



current 



and the current lags behind the impressed e.m.f. by an angle AOE = 

 such that 



The quantity L ~ - is the reactance of the circuit, while 

 Cp 



+ f Lp p - J is termed the impedance of the circuit. 



It is easy to see that the impedance, resistance, and reactance of a 

 circuit are capable of being represented by the throe sides of a right- 



angled triangle, one of whose angles corresponds to = tan l 



(the triangle OAE, in Fig. 10, may, to a suitable scale, be taken to 

 represent these three quantities). 



