78 ELECTRICAL MEASUREMENTS 



moment is due to the action of that field on the movable system. 

 This will be proportional to the current through the movable 

 coil. The field due to the fixed coil is proportional to the current 

 through it, so the total turning moment will be M = KJ F I M 

 K 2 HI M . If the coils are in series, the moment corresponding to 

 a current /, will be 



M = KJ 2 



Ki is a factor which depends on the dimensions and the numbers 

 of turns of both coils, and on the angle between their axes. K z 

 depends on the dimensions and number of turns of the movable 

 coil and on the position of the coil in the local field, H. 



To eliminate the effect of the local field two readings may be 

 taken, the current being reversed. In each case the torsion 

 head is adjusted until the original relative position of the coils 

 is reproduced. Then, if r is the torsion constant of the 

 controlling spring and 6 is the twist in the spring, 



Mi = KJ 2 + KzHI = r0i 

 M z = KJ 2 - K Z HI = T0 2 

 or 



If an alternating or regularly pulsating current is employed, 

 the turning moment passes through a cycle of values with each 

 complete period. As the natural time of vibration of the movable 

 system is much greater than the period of the current, the system 

 will take up a position dependent upon the average turning 

 moment, that is, the twist in the controlling spring will be given 



= * ' ^ f 



The subscripts F and M refer to the fixed and movable coils 

 respectively. T is the time of a complete cycle. 

 With alternating currents this becomes 



that is, the deflection when a torsion head is used, is proportional 



