5. The power factor.
The power factor is equal to the cosine of the angle of lag, that is, power factor = cos 53° = .602 (from table).
6. The true power.
The true power is equal to the apparent watts multiplied by the power factor, or
| true power | = | volts | × | amperes | × | cos φ | ||
| = | 100 | × | 20 | × | .602 | = | 1,204 watts. |
Ques. Prove that the power factor is unity when there is no resultant reactance in a circuit.
Ans. When there is no reactance, tan φ which is equal to reactance ÷ resistance becomes 0 ÷ R = 0. The angle φ (the phase difference angle) whose tangent is 0 is the angle of 0 degrees. Hence, the power factor which is equal to cos φ = cos 0° = 1.
Figs. 1,361 to 1,365.—Diagrams illustrating why the power factor is unity or one when there is no resultant reactance in the circuit, that is, when the circuit is resonant or has only resistance. The power factor is equal to the cosine of the angle of lag (or lead). In the figures this angle is BAC or φ and the value of the natural cosine AC gives the power factor. By inspection of the figures, it is evident that decreasing the reactance decreases the angle φ and increases cos φ or the power factor. The circular arc in each figure being at unity distance from the center A, the power factor with decreasing reactance evidently approaches unity as its limit, this limit being shown in fig. 1,365 where the reactance B'C' = 0.
Ques. What is the usual value of the power factor in practice?