THREE-VOLTMETER METHOD OP MEASURING POWER. 189 



resistance BG. Let vi, v%, and v be the corresponding instantaneous 

 value of the P.D. between the terminals of AB, BO, and AC 

 respectively. Then we have 



v = vi 4- v% 

 and squaring 



therefore 



where r is the resistance of the circuit BC. 



A_ B r 



*> * 



FIG. 78. 



Now, is the current flowing through AC, therefore the power 

 given to AB is 



where F", FI, F are the E.M.S. value of v, vi, and v% respectively, 

 and T is the periodic time of the currents. 



Therefore, the power given to an inductive circuit, AB, can be 

 measured by placing a non-inductive resistance, r, in series with it, 

 and applying the above formula, which necessitates taking simul- 

 taneous readings of three voltmeters. It can be shown that, for 

 the greatest accuracy, it is advisable to make FI equal to Fa. 



133. Three-ammeter Method. Let BC (Fig. 79) be 

 the inductive circuit, the power given to which is to be measured. 

 Let r be a non-inductive resistance in parallel with BC. 



Let A i, A 2 , A 3 be three ammeters arranged as shown, and 



