ELECTRIC CIRCUITS 



101 



In a two-pole alternating-current generator one cycle corre- 

 sponds to one revolution of the coil and 



/ = rev. per sec., 



and one electrical space degree is equal to one mechanical space 

 degree. With a p-pole alternator the e.m.f. passes through one 

 cycle for each pair of poles and the frequency is 



/ = ^ rev. per sec., 



and one electrical space degree is less than one mechanical space 



2 



degree in the ratio - 

 P 

 If a non-inductive resistance of R ohms is connected across the 



FIG. 74. Resistance in alternating-current circuits. 



terminals of the coil in Fig._74 an alternating current will flow in 

 the coil of instantaneous value 



sin 



U 



= I sin 8, 



(143) 



where I = ^ is the maximum value of the current. The cur- 

 n, 



rent and voltage waves pass through their zero and maximum 

 values together and are therefore in phase. They are represented 

 by the two curves in Fig. 74. 



72. The Average Value of a Sine Wave. The average value 

 of the ordinate of a sine wave i = I Q sin 6 can be found by in- 



