POWER AND POWER-FACTOR. 77 



cutting the semi-circle in D, then the line OD represents 

 the idle current in phase and magnitude. 



The figures inserted in the table above give a sample 

 reading, and Fig. 36 is the diagram corresponding to 

 these figures. 



The value of the angle of lag may be obtained by 

 measurement from the triangle, since the voltage of the 

 circuit is in phase with the energy current, and con- 

 sequently the angle D C is the angle of lag. < may 

 also be got from the value of the power factor ; thus 



watts ,. 



- = power factor = cos < 

 amperes X volts 



As a check on the accuracy of the figures inserted in 

 the table, it should be remembered that 



(energy current) 2 + (idle current) 2 =: (total current) 2 ; 

 indeed it is by the use of this equation that the idle current 

 would generally be calculated from the total and energy 

 currents. 



3-Voltmcter Measurement of Power. A direct useful appli- 

 cation may be made of the measurements made by 3 volt- 

 meters in Experiment II., page 29. It was shown how the 

 3-voltmeter measurements could be represented graphically 

 as the sides of a triangle of voltages. Since the voltage 

 in the non-inductive portion of the circuit is in phase 

 with the current, the angle of lag in the whole circuit is 

 the angle between the lines representing the voltage in 

 the non-inductive part and the total voltage respectively. 



Similarly, the angle of lag for the inductive portion is 

 the angle between the lines representing non-inductive 

 voltage and voltage of inductive portion. 



Thus, referring to Fig. 14, page 31, the voltage 

 represented by A C is in phase with the current in the 

 circuit, and consequently the angle C A B is the angle 

 of phase-difference between the current and total voltage, 

 i.e., the angle of lag for the whole circuit. Similarly, the 

 angle D C A is the angle of lag for the inductive portion 

 of the circuit. 



Since the pow r er in any circuit or portion of a circuit 

 is given by x E X cos 0, where C and E are the current 

 and voltage of the part considered, we have in the 

 diagram of the three electromotive forces all the 

 information necessary to determine the power in the 

 whole circuit and each portion of it, when we know also 

 the value of the current. 



