THEORY OF WATTMETER 45 



Consider in the first place the idetd wattmeter, in which the self- 

 inductance of the pressure or fine-wire circuit is negligible in com- 

 parison with the resistance, 

 and in which the fine-wire M r t 



circuit is also utterly devoid ffiffl x/WWWWWVWW\A 



of capacity. The current in [ 

 this circuit will then be in "" ~~* 

 phase with, and proportional 

 to, the p.d. Hence the instan- 

 taneous couple acting on the F A 

 instrument will be proportional FIG. 31. Connections of Wattmeter, 

 to the product p.d. x current, 



i.e. to the power, and the mean couple to the mean power. The 

 angle of torsion will therefore be proportional to the mean 

 power. 



In the actual instrument, the self-inductance of the fine-wire 

 circuit is made as small as possible by using a coil of the smallest 

 possible number of turns. The capacity of this circuit is reduced to 

 a practically negligible amount by winding the non-inductive resist- 

 ance bifilarly in sections, which are then connected in series with 

 each other. 



It is more difficult in practice to reduce the self-inductance to a 

 negligible amount than the capacity, and it is important to investigate 

 what effect the presence of a small amount of self-inductance may 

 have on the reading of the instrument. 



Let R, L denote the resistance and self-inductance of the load 

 respectively, and let r, I stand for the corresponding quantities in the 

 fine-wire circuit of the wattmeter. If V = p.d., I = current in main 



circuit, then, denoting tan" 1 by 0, and tan" 1 *- by 0, we have 



XV 



true power w = VI cos $ ( 7) 



and if I were negligible the wattmeter reading would correspond to 

 VI cos (ft. The effect of I is a twofold one : it reduces the current in 



7* 



the fine-wire circuit in the ratio ^a/a* an( ^ * fc ^ urfc ^ ier causes the 



current to lag behind the p.d. by an angle 0. The first effect reduces 

 the couple in the given ratio, while the second is obviously equivalent 

 to a change in the power factor of the load from cos ^> to cos (<j> 0). 

 Thus the reading of the wattmeter will be 



w = - - VIr - . cos U - 0) = VI cos cos (A - 0) 

 X/r*+^ 



