64 POWER AND POWER-FACTOR. 



Energy and Idle Voltage. 



It has been shown already that the electromotive force 

 of the circuit consists of two components which differ by a 

 quarter of a period in phase (see page 18). One of 

 these components (equal to C R when there are no iron 

 losses in the circuit) is in phase with the current, the 

 other (equal to 2 irn L C) is a quarter of a period out of 

 phase with it. 



It has also been stated that the average product of the 

 instantaneous values of the current and volts is zero when 

 the variations of current and voltage have a quarter period phase 

 difference, whereas the value of this product is numerically 

 equal to the product (current x voltage) when the current 

 and voltage are in phase. 



Hence the two components of the voltage correspond 

 respectively to the portion of the voltage which does not 

 affect the power of the circuit, and the portion which when 

 multiplied by the value of the current represents the total 

 power of the circuit. 



These two components may be suitably called the " Idle " 

 and "Useful," or "Energy" components of the electromotive 

 force. 



Hence power given out by current in circuit = useful 

 component of electromotive force x current = energy voltage 

 x C. 



Referring to Fig. 29 representing the three electro- 

 s' f 

 motive forces of the circuit cos F E = - f 



U h 



or F E = E cos F E 0; 



but the angle F E is the angle of phase difference between 

 the current and voltage of the circuit = 9 



Hence F E = E cos 9 



or energy voltage = total voltage x cos $ 

 or useful component = total voltage x cos . 



Consequently if V = total voltage of circuit, the power 

 given out = C x energy voltage = C x V cos $. 



But the power of the circuit = C x V x power-factor, 

 and consequently we have power-factor = cos 0. 



The power-factor of a circuit is the cosine of the angle 

 of phase difference between current and voltage. 



