CH. XIII] ALTERNATING CURRENT UNITS 485 



674. Watts with alternating current. With alternating as 

 with direct current, the instantaneous watts are equal to the pro- 

 duct of the instantaneous volts by the instantaneous amperes. 



As the voltage and amperage with alternating current vary 

 from instant to instant over the entire cycle, it follows that the 

 instantaneous watts must also vary from instant to instant. To 

 obtain the average watts over an entire cycle, the arithmetical 

 mean of the instantaneous watts is taken. This average of the 

 watts may be anything between zero and the product of the mean 

 effective volts times the mean effective amperes, depending on the 

 character of the circuit, i. e., whether the circuit contains resistance 

 only or whether it contains both resistance and inductance. 



675. Power factor. When alternating current is used with 

 inductance in the circuit as described in 736 (where an inductor 

 or choke-coil is put in series with the arc) the power transformed 

 into heat or work, and hence which must be supplied to the dynamo 

 by coal or other fuel is less than the product of the mean effective 

 volts by the mean effective amperes. This is because most of the 

 energy required to magnetize the iron core of the inductor when the 

 current is increasing is returned to the line when the current is 

 decreasing. In the case mentioned the line voltage was no; at 

 the arc the voltage was 34, and 55 amperes were drawn. The power 

 consumption at the arc, which is unable to return any absorbed 

 energy to the line, is the product of the volts by the amperes, i. e., 

 34 x 55 = 1,870 watts. In this case the power factor is unity. In 

 the case of the entire circuit, however, by multiplying the line 

 voltage by the amperage, i. e., 1 10 x 55 we get 6050. A wattmeter 

 would register only the 1870 watts consumed at the arc. The 

 power factor is the value by which we must multiply the product of 

 volts x amperes in order to get watts. Thus, if we multiply 6050 

 by .3 1 we get 1870. The power factor is of course obtained in prac- 

 tice by dividing the watts by the product of volts by amperes, i. e., 

 P. F. = Watts -4- Volts x Amperes; and Watts = Volts x Amperes x 

 Power factor. Nothing comparable to this effect is possible with 

 direct current, that is, with direct current the power factor is always 

 unity. 



