80 POWER AND POWER-FACTOR. 



V, 2 = V z 2 + F 3 2 - 2 F 2 V 3 cos *, 



but F 2 = GE where E is the resistance of the non-induc- 

 tive portion of the circuit. 



... Fi 2 = F 2 2 + F 5 2 - 2 E C F 3 cos <t>. 



Since the total power of the circuit = CVs cos <f>, we 

 have 



Power in circuit = 



T7"2 _|_ T/ 2 _ J72 







2t If 



The power in the inductive portion r is obtained by 

 subtracting the watts spent in the non-inductive portion 

 from this expression. The watts in the non-inductive 



F 2 

 resistance are * 



Hence watts in inductive part of circuit 



F 5 2 - F 2 2 - F t 2 

 2E 



In making a measurement of the power of the circuit 

 it is not necessary to measure the current if the value of 

 the non-inductive resistance is known. It will often be 

 the easiest method of determining this resistance to put 

 an ammeter in the circuit, as shown in the diagrams 

 given. 



For greatest sensitiveness of measurement the 

 readings of the voltmeters connected to the inductive and 

 non-inductive parts of the circuit should be as nearly 

 equal as possible. 



3-Ammeter Measurement of Power. This method is 

 analogous to the preceding, but employs three ammeters 

 instead of three voltmeters for making the measurement. 

 From the readings, a triangle of currents, instead of a 

 triangle of voltages, gives the construction for deter- 

 mining the angle of lag. 



In this case a non-inductive resistance must form a 

 parallel circuit to the inductive part of the circuit, and 

 must be added if not already part of the connections. 

 The connections for making the measurement are those 

 given in Diagram 32, page 72. 



As in the previous case, the following experiment is 

 arranged for a comparison between the measurement 

 made by this method, and the measurement with a 

 wattmeter : 



