POWER MEASUREMENT 



311 



The deflection of the instrument is proportional to the mean 

 product of the instantaneous values of I P and I L , therefore, 



KD 



= -,- ri L i P dt = 

 T Jo * 



cos (8 L - OP). 



So the apparent power or the scale reading is 







R P KD = I L 



cos (0 L - 



=P 



(2) 



The true power, that is the power which would be read from 

 the scale if there were no reactance in the potential circuit, 

 is given by 



P L +H C = -~cos *< ( 3 ) 



FIG. 180. Pertaining to effect of inductance in the potential circuit of a 



wattmeter. 



A correction to be subtracted from the apparent power in 

 order to obtain the true power may be determined, for by (2) 



I L V cos B P I L V 



Pw = ~ - COS (0 L - 6 P ) = - 



' P 



(cos 2 BP cos B L -\~ cos B P sin B P sin L ) 

 P ' IV 



- "" ta " 8 " si " '* 



In portable instruments the angle B P is a very small fraction of a 

 degree but in commutating watt-hour meters, such as were 

 formerly used on alternating-current circuits, it may be as large 

 as 2. Using the values of the current and voltage given by 



