Fig. 1,343.—Marine analogy of power factor. A ferry boat in crossing a river to a slip C would head for some point B up stream from C to allow for the effect of the tide. Under such conditions the actual motion (referred to the water) would be from A to B, and the apparent motion, from A to C. Accordingly, the energy expended in propelling the boat from A to B in still water, will propel it from A to C when the tide is running in the direction of the arrow. The effect of the tide is the same as that of inductance or capacity in an alternating circuit, that is, it puts the applied force or thrust (impressed volts) out of phase with the motion of the boat (amperes), this phase difference being indicated by the angle BAC or φ. Now, work (watts) is the product of two factors, pressure (volts) and distance (amperes); accordingly, the apparent work done in propelling the boat from A to C is the product of the thrust of the paddle wheels multiplied by AC, which in analogy corresponds to the product of voltmeter and ammeter readings at the alternator, called "kva." Actually, however, the power is only applied from A to B, the boat being carried sidewise by the tide, as it crosses, a distance BC which represents no energy expended by the paddle wheels. In analogy, the actual power, expended in propelling boat from A to B corresponds to the wattmeter reading in an alternating current power circuit. To obtain the actual work done on the boat, the product of its apparent motion × thrust must be multiplied by a coefficient or power factor because the thrust is applied at an angle to the apparent motion, the power factor being equal to the cosine of this angle, (φ) or AB ÷ AC. Similarly, when there is phase difference between pressure and alternating current, the voltmeter and ammeter readings must be multiplied by the power factor or cos φ to give the output of an alternator available for external work, the excess power indicated by ammeter and voltmeter readings, performing no external work, but causing objectionable heating of the alternator.
Ques. Upon what does the power factor depend?
Ans. Upon the relative amounts of resistance inductance and capacity contained in the circuit.
Ques. How does the power factor vary in value?
Ans. It varies from one to zero.
The power factor, as will be shown later, is equal to the cosine of the angle of phase difference; its range then is from one to zero because these are the limiting values of the cosine of an angle (neglecting the + or-sign).
Ques. What is the effect of lag or lead of the current on the power factor?
Ans. It causes it to become less than one.
