188 TREATISE ON ALTERNATING CURRENTS. 



Also, the power, as measured by the wattmeter, is the scalar 

 product of ii and ri, that is 



Measured power = scalar product of 



Therefore 



TV T 



Measured power x T T \ a 



r(tTi + jrZZi) ri 2 -f 



= true power. 



The correcting factor is therefore 



where T=~ and 7\ = -- are the time constants of the two circuits 

 r n 



respectively. 



It is seen from this that if the thin coil of a wattmeter has 

 any self-induction the correction factor depends upon the self- 

 induction of both circuits, unless 



That is, the correcting factor will be unity, if 



T(T- Ti) = 

 that is, if 



T=0 

 or 



T=T, 



Since, however, TI is usually unknown, though it can be 

 determined, it is best to wind the thin coil of the wattmeter so 

 that T is as small as possible. This is done by inserting in series 

 with the thin coil a hi^h non-inductive resistance. 



OTHER METHODS OF MEASURING POWER. 



132. Three-voltmeter Method, Let, in Fig. 78, 

 AB be an inductive circuit in series with a non-inductive 



