276 ELECTRICAL EQUIPMENT 



formers and other electric apparatus using two windings and an 

 iron core, the ratio of turns, other factors remaining the same, will 

 be approximately inversely as the square root of the frequency. 

 The lower the frequency the larger the flux, and the larger the 

 number of turns for the same voltage. Therefore, transformers 

 increase in cost and weight as the frequency decreases. 



The regulation of 25-cycle transformers is not quite as good as 

 for 60-cycle on account of the increased drop, due to the great 

 number of turns and their increased mean length, and the effi- 

 ciency is also somewhat less. 



Operating 25-cycle transformers on a 60-cycle circuit decreases 

 the flux density and the core loss. Operating a 60-cycle trans- 

 former on a 25-cycle circuit increases the density and core loss, and, 

 in general, gives a prohibitive exciting current. Frequency also 

 enters into the mechanical forces to which a transformer may be 

 subjected, as the reactance increases with the frequency, and, 

 while the mechanical force varies directly as the square of the 

 current, a 25-cycle transformer operating on a 60-cycle circuit 

 would be subject to about one-half the mechanical strains on short- 

 circuit. The limit of reactance in a transformer is from 8 to 10 

 per cent at 60 cycles and somewhat higher at 25 cycles. 



Transmission Lines. Transmission lines are designed from 

 considerations of regulation and efficiency and, as explained more 

 fully under " Voltage," the regulation is better as the frequency is 

 lower, and so for commercial work 25 cycles is preferable to 60 

 cycles, considering the line alone. The capacity current plays, 

 as stated, also an important part with small units and high volt- 

 ages, rendering it often impossible to throw one machine on the 

 line alone. Both the reactance and the capacity current of the 

 line are proportionate to the frequency as shown by the following 

 equations: 



Reactance = 2irfL ; 



Capacity current = 2TrfCE', 



The resistance of wires and cables carrying alternating cur- 

 rents is also affected by the frequency, in that the current is not 

 distributed uniformly over the cross-section of the conductors, the 

 current density being higher near the periphery. This is known as 

 " skin effect " and results in an increased resistance. The effect 



