POWER AND POWER-FACTOR. 57 



If the current and electromotive force ,act in opposing 

 directions in the circuit, their product must be considered 

 as negative, i.e., the power represented by the current is 

 negative. This is illustrated in Fig. 25, which shows a curve 

 of current C and a curve of voltage V which differ in phase 

 by 30. The power of the circuit varies continuously, since 

 the product of current and volts changes with these 

 quantities. A third curve of watts W obtained by calculating 

 the product of current and volts is drawn, and represents the 

 fluctuation of the power in the circuit. 



Since ordinates below the base line represent quantities 

 directed in a negative direction along the circuit, the power 

 curve passes below the line, i.e., represents negative watts 

 when given by the product of two quantities on opposite 

 sides of the base line (since the product of a positive quantity 

 by a negative quantity is always negative). 



The meaning of this negative power is that when the 

 power of the circuit is negative, the circuit is not receiving 

 power from the generator to be spent in heating conductors 

 driving motors, &c., but is at such times giving back power 

 to the generator (or to some part of the circuit) in virtue of 

 the self-induction (analogous to inertia) possessed by the 

 circuit. When the watts are negative, the power is therefore 

 actually to be considered as given back by the circuit to the 

 generator to assist in driving it. Consequently the energy 

 delivered to the resistances or apparatus in any portion of 

 the circuit is the mean arithmetic sum of the power of the 

 circuit multiplied by the time of its duration. 



The Average Power developed in the circuit is the average 

 value of the product (amperes x volts) in the circuit. This 

 value is shown in Fig. 25 by a horizontal dotted line A B, 

 obtained by adding together the ordinates of the curve of 

 watts corresponding to each vertical line of the squared 

 paper and dividing by the number of these ordinates. 

 Ordinates below the base line must be subtracted from the 

 sum of the ordinates above the line. The value of the average 

 power is seen in this case to be 430 watts. 



The average value of the power in a circuit can be 

 measured directly by a wattmeter. 



The wattmeter has two coils, one carrying the current 

 of the circuit, and one connected in the same manner as a 

 voltmeter so as to carry a small current proportional to 

 the voltage of the circuit to which it is connected. 



