204 ELECTRICAL MACHINERY 



OB which represents a current in an inductive circuit, on 

 which the voltage OA is impressed. 



If the equation of the voltage is written e = E m cos tot 

 then evidently the proper equation for current (referred 

 to the same time origin as the e.m.f.) is i = \ m cos(^t <j>) and 4> 

 in the phase difference of current and e.m.f. 



Power Factor. The power being used at any instant 

 in an a-c. circuit is given by the product of the values of 

 e.m.f. and current at the instant considered. It is proved 

 in elementary texts on alternating currents that the power 

 used in any circuit, in terms of virtual voltage and current 

 is given by the formula Watts = El cos cj>. 



FIG. 123. Current and Voltage in Same Phase. 



The product, El, is sometimes called apparent power 

 and evidently cos <j> is that quality ly which the apparent 

 power must be multiplied to give the true power. It is there- 

 fore called the power factor of the circuit. 



48. Active and Reactive Components of Voltage and 

 Current. It is generally necessary to use the expression 

 " voltage in phase with current " or " in-phase voltage " 

 and similar expressions. When the voltage and current 

 are represented as vectors, we resolve one on the other 

 and so get two components at right angles to one another. 

 In Fig. 124 the two possible schemes are represented. 



In (a) the voltage OE is projected on the current vector 

 01. The component OA is in phase with the current and 



