THE MAGNETIC CIRCUIT [ART. 71 



Alternating-Current Electromagnets. The preceding formulae are 

 deduced under the supposition that the magnetic field is excited 

 by a direct current. They are, however, applicable also to alter- 

 nating-current electromagnets, because the pulsations in the 

 current merely cause the energy to surge to and from the magnetic 

 circuit, without any net effect, so far as the average stored energy 

 and the mechanical work are concerned. The average stored 

 energy corresponds to the effective values of the current and the 

 flux. 



In practice two types of alternating-current electromagnets 

 are of importance, namely, those operating at a constant voltage 

 and those operating at a constant current. As an example of 

 the first class may be mentioned the electromagnets used for 

 the operation of large switches at a distance (remote control); 

 the windings of such electromagnets are usually connected directly 

 across the line. Constant-current magnets are used in the 

 operating mechanism of alternating-current series arc-lamps. In 

 an A. C. electromagnet practically all of the voltage drop is 

 reactive and hence proportional to the flux. 



In a constant-potential electromagnet the effective value of 

 the equivalent flux is the same for all positions of the plunger 

 (neglecting the ohmic drop in the winding). Therefore, formula 

 (185) holds true. Let e be the effective value of the constant 

 voltage, or more accurately the reactive component alone, and 

 let / be the frequency of the supply. Then, e= ZnfLiii = 2nfL 2 i 2 , 

 so that the formula for the pull becomes 



(190) 



For a constant-current A.C. electromagnet eq. (186) applies; 

 introducing again the reactive volts e 1 = 27r/L 1 'i and e 2 =2nfL 2 i, 

 we get 



(191) 



In both cases the mechanical work performed is proportional 

 to the difference in the reactive volt-amperes consumed in the 

 two extreme positions of the moving part. 1 



1 For further details in regard to electromagnets consult C. P. Steinmetz, 

 Mechanical Forces in Magnetic Fields, Trans. Amer. Inst. Elec. Engs., Vol. 

 30 (1911), and the discussion following this paper; also C. R. Underhill 

 Solenoids, Electromagnets, and Electromagnetic Windings (1910), chapters 6 



