Figs. 2,125 to 2,128.—Parallelograms of forces showing increase in magnitude of the resultant of two forces, as their difference of direction, or electrically speaking, their phase difference is diminished. The diagrams show the growth of the resultant of the two equal forces OA and OB as the phase difference is reduced from 165° successively to 120, 60, and 15 degrees.
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
AB = √((OA)2 + (OB)2) (1)
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.
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?