40 ELEMENTS OF ELECTRICAL ENGINEERING. 



coils is balanced by moving a weight or by twisting a helical 

 spring which is attached to the movable coil. In this case the 

 reading of the instrument is the distance that the weight is 

 moved, or the angle through which the spring is twisted. 



The electrodynamometer when standardized by direct current in- 

 dicates effective values of alternating current. This is evident 

 when we consider that the force action between the coils is pro- 

 portional to the square of the current, or equal to a constant, k, 

 times the square of the current, and that the force action, kC 2 y 

 due to a direct current C must be equal to the average force 

 action, kx average/ 2 , due to an alternating current i\ if C 

 and i produce the same deflection, kC 2 must be equal to 

 k x average i 2 , or C= i/ average i 2 . 



The electrodynamometer is the most reliable form of alternat- 

 ing-current ammeter. 



When the electrodynamometer is used as a voltmeter, its coils 

 are made of fine wire, and an auxiliary non-inductive resistance is 

 connected in series with the coils. 



When the inductance of the electrodynamometer coils is small * 

 the instrument indicates effective values of alternating electromotive 

 force accurately when it has been calibrated by direct electromotive 

 force. This is evident when we consider that the current i in 

 a non-inductive circuit is at each instant equal to efR, where 

 R is the resistance of the circuit, and e is the value at the given 

 instant of the electromotive force across the terminals of the cir- 

 cuit ; and when we consider, furthermore, that the average de- 

 flecting force due to an alternating electromotive force, namely, 

 kjR 2 x average e 2 (= k x average i 2 if the circuit is non-induc- 

 tive) must be equal to the constant deflecting force kjR 2 x & 2 

 (= k x current 2 ) due to a direct electromotive force S which 

 produces the same deflection. 



The effect of the inductance of a voltmeter is to make an in- 

 strument which has been calibrated by direct electromotive force 



*That is, when the reactance wZ is small compared with the resistance. See 

 chapter IV. 



