IO 



ALTERNATING CURRENTS 



Since L is negligible, the impressed e.m.f. is, by equation (1), 

 equal to 



e = ri = rl 



The impressed e.m.f. is thus in phase with the current, and the vectors 

 corresponding to the impressed e.m.f. and the current in a vector 

 diagram lie along the same straight line, as shown in Fig. 5. Further, 

 considering r.m.s. values of e.m.f. and current, we see that 



e.m.f. 



current = . . 



resistance 



Let us next consider another extreme case that, namely, in 

 which the self-inductance of a circuit is so high that its resistance 

 may be neglected in comparison. An example of such a circuit is 

 furnished by a coil consisting of a very large number of turns of fairly 

 thick wire. Let L stand for the inductance of the circuit, the current 

 being as before given by (2). Then since r is by supposition negligible, 

 (1) gives 



cfo' _ d 



= pLI cos pt 



Let OP = I in Fig. 6 represent the current vector. Draw OR at 

 right angles to OP, making OR = pLI. At any instant t, the pro- 



CURREWT. 



FIG. 5. Vector Diagram for Pure 

 Resistance. 



FIG. 6. Vector Diagram for Pure 

 Inductance. 



jection of OP on the vertical, gives the value of the current, while at 

 the same instant the projection of OR, which is given by OR cos 

 pt = pLI cos pt = e, represents the value of the impressed e.m.f. 

 Thus OR is the e.m.f. vector, and we see that there is a phase differ- 

 ence of * or 90 between the impressed e.m.f. and the current, the 

 



current lagging behind the impressed e.m.f. When two sine waves 

 differ in phase by 9 , they are said to be in quadrature with each 



