82 POWER AND POWER-FACTOR. 



Measurement of Power by Three Ammeters. 



The watts may be calculated after drawing a 

 triangle of currents for each set of readings from the 

 formula : Power = C V cos <. The value of <j> is the 

 angle between the line representing the current in 

 the non-inductive branch and in the circuit for which the 

 power is to be calculated. 



As in the last experiment, the results should be 

 checked by a calculation. In this case the calculation 

 depends upon the formula obtained as follows : 



In the triangle of currents (see Fig. 33, p. 73) we have 

 by trigonometry 



d 2 = C 2 2 + C? - 2 C 2 C z cos <. 



Tjl 



Also C 2 =-p- where E is the voltage at the terminals 



JK 



of the branch circuits and R is the value of the non- 

 inductive resistance. 



2 



. r\ 2 r< 2 i 



. , V, = o 2 -j- 



- CJS COS 



But Ci,E cos tf> is the total power given to the branch 

 circuits. Hence 



TD _ 



Total power in branch circuits = - |C 2 2 + (7 3 2 C* I 

 The power in the non-inductive branch = C^R. 

 .'. Power in inductive branch =-o-[ 3 ~~ 2 ~ 1 J 



For maximum sensitiveness the currents in the two 

 branches should be approximately equal. 



If the value of the resistance in the non-inductive 

 branch is known, it is not necessary to employ the volt- 

 meter. Usually the addition of the voltmeter forms the 

 simplest method of determining the resistance. 



