According to this principle, if two alternating pressures have a phase difference of 90 degrees they may be represented in magnitude and direction by the two sides of a right angle triangle as OA and OB in fig. 2,129; then will the hypotenuse AB represent the magnitude and direction of the resultant pressure. That is to say, the resultant pressure
EXAMPLE.--A two phase alternator is wound for 300 volts on one phase and 200 volts on the other phase, the phase difference being 90°. If one end of each winding were joined so as to form a single winding around the armature, what would be the resultant pressure?
By calculation, substituting the given values in equation (1),
Resultant pressure = √(300² + 200²) = √(130,000) = 360.6 volts.
This is easily done graphically as in fig. 2,129 by taking a scale, say, 1" = 100 volts and laying off OA = 3" = 300 volts, and at right angles OB = 2" = 200 volts, then by measurement AB = 3.606" = 360.6 volts.
[Illustration: FIG. 2,129.--Method of obtaining the resultant of two component pressures acting at right angles by solution of right angle triangle. The equation of the right angle triangle is explained at length in Guide No. 5, page 1,070.]
~Ques. When the two pressures are equal and the phase difference is 90°, is it necessary to use equation (1) to obtain the resultant?~
Ans. No. The resultant is obtained by simply multiplying one of the pressures by 1.41.
This is evident from fig. 2,130. Here the two pressures OA and OB are equal as indicated by the dotted arc. Since they act at right angles, OB is drawn at 90° to OA. According to the equation of the right angle triangle, the resultant AB = √(1² + 1²) = √2̅ = 1.4142 which ordinarily is taken as 1.41.
_This value will always represent the ratio between the magnitude of the resultant and the two component forces, when the latter are equal, and have a phase difference of 90 degrees._
~Forms of Circuit.~--Alternating current systems of distribution may be classed, with respect to the kind of circuit used, in a manner similar to direct current systems, that is, they may be called series, parallel, series parallel, or parallel series systems, as shown in figs. 2,131 to 2,134.
[Illustration: FIG. 2,130.--Diagram for obtaining the resultant of two equal component pressures acting at right angles.]