ALTERNATING CURRENT MEASUREMENTS. 41 



indicate less than the effective value of an alternating electromo- 

 tive force, the error being the greater the higher the frequency. 

 Nevertheless the electrodynamometer type of voltmeter is the 

 most generally satisfactory and reliable type of alternating-cur- 

 rent voltmeter. 



A disadvantage of the electrodynamometer (ammeter or volt- 

 meter) as compared with the plunger type of instrument is its 

 greater cost. 



Inductance error of the electrodynamometer when used as a voltmeter. The fol- 

 lowing discussion is limited to the case of harmonic electromotive force and harmonic 

 current, and it presupposes a knowledge of Chapters III and IV. Let S be a direct 

 electromotive force which gives the same deflection as an alternating electromotive force 

 whose effective value is E, and whose frequency is/" cycles per second, or u (=27rf) 

 radians per second. Since the deflections are the same, the square of the direct cur- 

 rent produced by S, (8 2 ffi 2 ), must be equal to the average square of the alternating 

 current [^/(^-f- w 2 Z 2 )] produced by , that is, 



whence we find 



in which E is the true effective value of a harmonic alternating electromotive force of 

 a frequency of u radians per second, S is the voltmeter reading produced thereby^ 

 R is the resistance of the voltmeter, and L is the inductance of the electrodynameter 

 coils. 



14. The electrostatic voltmeter. Two insulated metal plates 

 connected to the terminals of a battery, or to any source of elec- 

 tromotive force, attract each other with a force which is exactly 

 proportional to the square of the electromotive force. This 

 principle is applied in the electrostatic voltmeter which consists 

 essentially of a fixed metal plate and a delicately poised or sus- 

 pended metal plate which carries a pointer, the two plates being 

 connected to the terminals of the source of the electromotive force 

 to be measured. 



Suck an instrument, when calibrated by direct electromotive 

 force, indicates effective values of alternating electromotive force. 

 This is evident when we consider that the steady force action, 

 ks 2 , due to a direct electromotive force S must be equal to the 



