ELECTRICITY METERS 475 



torque of the brake, or K D u', where w' is the angular velocity of 

 the disc. The term 



represents the drag due to the motion of the disc through the 

 alternating fields in the air gaps. It will vary with the load on 

 the meter, and be a source of error, but by correct design this 

 error may be made negligibly small, and the angular velocity of 

 the movable element becomes 



a/ = KVI sin ( 2 - fa). 

 But the potential circuit is highly inductive, so (see Fig. 262) 



co' = KVI cos (0 + a) (6) 



where 6 is the power factor angle of the load and a is the departure 

 from exact time quadrature of the useful potential-coil flux and 

 the potential applied to the load (see page 453). 



If the meter is properly lagged, that is, if a = 0, the angular 

 velocity of the disc is proportional to the power and the total 

 number of revolutions executed in any time interval is pro- 

 portional to the kilowatt-hours of energy supplied during that 

 time. 



The Lag Adjustment. Exact time quadrature of the useful 

 potential-coil flux and the voltage applied to the load is obtained 

 by the use of a lag coil, LC, which is wound about the potential- 

 pole tip. The circuit of this coil is completed by the resistance 

 Ri which is adjusted until the desired phase relation (A = 90) 

 is established. A simplified diagram of the potential circuit 

 is shown in Fig. 272 A. It will be seen that the arrangement is 

 equivalent to a transformer with large leakage reactances. 

 For simplicity a 1 : 1 ratio is assumed. The disc, which serves 

 as the rotor, projects into the air gap, a^ and is cut by the total 

 flux in the gap, <i> 2 . The mutual flux which cuts the primary 

 and secondary is $ M and the primary and secondary leakage 

 fluxes are <J> L1 and $^2, respectively, <J>z,2 being the leakage flux 

 which cuts through the disc. The total flux through the primary 

 is <J>i. When the secondary is open the angle A is less than 90 

 due to the IR drop in the potential coil. When the secondary 



