so that 



GENERATION OF ALTERNATING E.M.F.S. 



= AB cos pt 



19 



The E.M.F. induced in the moving circuit is, therefore, given 

 by- 



dN 



e= ~^t 

 mABpswpt ...... (1) 



which is the rate of change of the magnetic flux through the 

 circuit. 



The value of e is therefore zero when pt is or any multiple 

 of 2?r; it then becomes positive and attains a maximum value 



ABp when pt is ^, or ^ + any multiple of 2?r ; it becomes zero 



-j 2t 



vrhenpt = TT, or any odd multiple of ?r, and then becomes negative, 

 and is a negative maximum, and equal to ABp when 



o 



pt = _- -f any multiple of 2?r 

 a 



As increases from to 2xr the coil rotates through one 

 complete revolution and the value of e goes through a complete 

 cycle of changes which repeats itself in every succeeding 

 revolution. 



If the coil consists of n complete turns each having an area 



FIG. 3. 



equal to A, and arranged so that all the turns are placed in series 

 and form one circuit of n loops, the induced E.M.F. is increased 

 7i -fold, and is given by 



e = nABp sin pt (2) 



