100 ELECTRICAL ENGINEERING 



(3) it is positive and has reached its maximum value since the 

 conductors are cutting perpendicularly across the flux; in (4) it is 

 positive and decreasing; in (5) it is zero; in (6) it is.;tiegative and 

 increasing; in (7) negative and maximum; in (8) negative and de- 

 creasing and in (1) is zero again, having gone through one com- 

 plete cycle. This cycle is represented in Fig. 73. 



If < = the maximum flux inclosed by the coil, n = the number 

 of turns on the coil and co = the angular velocity in radians per 

 second, then at time t sec. after the position of maximum in- 

 closure the coil has moved through angle 6 = co radians, and the 

 flux inclosed is 



<f> = < cos coZ; 



the e.m.f. generated in the coil at this instant is 



e = n -r- (< cos coZ) 



= OM<|> sin ut absolute units 



= con<l> 10~ 8 sin at volts ...... (139) 



When 6 = ~ , the e.m.f. has its maximum value 



EQ = 0)71$ 10~ 8 VOltS, 



and therefore 



e = EQ sin co/; ......... (140) 



and the e.m.f. generated in the coil varies as a sine wave. 



The number of cycles through which the e.m.f. passes in one 

 second is called its frequency and since one cycle represents 360 

 electrical degrees, the frequency may be expressed as 



/ = ^cycles, ...... (141) 



and therefore 



CO = 27T/. 



Substituting this value of co in equation 139 gives 

 e = 2 irfn3> 10~ 8 sin 2 irft 

 = EQ sin 6, 



where 6 = 2 irft is the angle turned through in time t sec. after the 

 position of zero e.m.f.; the maximum value of the e.m.f. is 



EQ = 27r/n$10- 8 volts ....... (142) 



