460 ELECTRICAL MEASUREMENTS 



The armature current will be 

 V - kkrlo V - 



7 = - 



The driving torque due to the main coils may be represented 

 by K F II a and that due to the light-load coils by Kp>I<?. As the 

 meter is operated at a constant voltage and the torque due to the 

 light-load coil is small, it is allowable to consider this quantity 

 as constant; it will be denoted by K s . The total accelerating 

 torque is 



The total retarding torque is that due to the mechanical fric- 

 tion of the meter (including windage) plus that due to the mag- 

 netic brake. The friction torque has a certain initial value, 

 denoted by K M , and increases more rapidly than the speed; its 

 value may then be represented by K M + K M >u> 2 . The brake torque 

 is proportional to the angular velocity of the disc and if the tem- 

 perature of the disc and the magnets is constant, may be expressed 



. k D h 2 u 



by ^- = K D u. (2) 



Consequently the total retarding torque is 



K M + Kot* + K,rf (3) 



For steady motion the accelerating and retarding torques must 

 be equal. Equating (1) and (3) gives for the angular velocity of 

 the disc, 



co = K^VI - #2/ 2 co + K' s - K' M - K'M'U* (4) 



The terms on the right-hand side of the equation which involve 

 co are small corrections due to the back e.m.f. and the change of 

 friction torque with the speed. 



It is seen that if the light-load coil is adjusted so that at no- 

 load the meter is just on the point of starting (K r M very slightly 

 greater than K's), the angular velocity of the armature will be 

 practically proportional to the power supplied to the load; and 

 it at once follows that the total number of revolutions, N, exe- 

 cuted by the armature in a given time is proportional to the 

 energy supplied to the load during that time. 



