PHASE METERS 533 



The current in coil A is supposed to be controlled by a pure 

 resistance, and consequently is in phase with the applied voltage 

 V. The current in coil B is supposed to be controlled by a pure 

 inductance, and hence is in quadrature with the voltage V. 



The currents are taken into the movable system at the pivot, 

 through flexible connections of annealed silver foil which resemble 

 ordinary controlling springs in appearance but which exercise 

 no appreciable torque on the system. 



When no currents are flowing, the crossed coils are perfectly 

 neutral and will remain in any position to which they are turned. 

 The position of the crossed coils from which the deflections are 

 reckoned is that assumed by them when the device is applied 

 to a load of power factor unity. In that case the planes of coils 

 A and F will coincide, for as the currents in B and F are in 

 quadrature, on account of the inductance L, the average turning 

 moment on B is zero. 



In general, on the passage of currents through the coils F, A and 

 B, a field will be set up by F, and the coils A and B which form 

 the movable element will both experience turning moments. 

 As A and B are rigidly connected, the movable element will turn 

 to such a position that the resultant moment acting on it be- 

 comes zero. The deflection, D, from the initial position occupied 

 by the coils when the power factor is unity, will be equal to the 

 power-factor angle of the load. 



It will be assumed that the coil F is so large compared with 

 A and B that the crossed coils move in a sensibly uniform field; 

 also that the circuits of A and B are inductionless and resist- 

 anceless respectively. If the P.D. wave be taken as the datum 

 for measuring phase displacements, the turning moment acting 

 on coil A will be, at any instant, 



K A [I sin (ut - 0)]|j2 sin coJ sin D, 



where K A is a constant depending on the windings. 



The turning moment on coil B will be, at any instant, 



K B [I sin ( - 0)][j^ sin (coZ - 90)] sin [D + 90]. 



The currents in the coils are such that A and B tend to turn in 

 opposite directions. When the movable system has come to 



