Mathematics for Electrical Calculations, Power Factor Correction, and Harmonics Cũng như các 100 pounds (lb) vũ lực mà một đứa trẻ tác động khi kéo một đối tượng đối với các phía đông, hoặc hướng x, thông qua một sợi dây thừng, không có thể được bổ sung trực tiếp các lb 150 của lực lượng mà một đứa trẻ riêng biệt tác động đồng thời kéo cùng một đối tượngvề hướng bắc, hoặc y, hai kéo làm việc cùng nhau hướng tới mục tiêu kéo các đối tượng trong một hướng có phần theo hướng x và có. | Chapter 3 Mathematics for Electrical Calculations Power Factor Correction and Harmonics Just as the 100 pounds lb of force that a child exerts when pulling an object toward the east or x direction through a rope cannot be added directly to the 150 lb of force that a separate child exerts simultaneously pulling the same object toward the north or y direction the two pulls do work together toward the goal of pulling the object in a direction that is somewhat in the x direction and somewhat in the y direction. The y direction is depicted in vector geometry as j and the y direction is depicted as -j. To resolve the value of the resulting force that is exerted onto the object vector addition is used. Changing Vectors from Rectangular to Polar Form and Back Again Vector values are written in two different ways to represent the same values 69 Copyright 2001 by The McGraw-Hill Companies Inc. Click here for Terms of Use. 70 Chapter Three 1. Polar coordinates 100 z 0 2. Rectangular coordinates 100cos0 j 100sin0 In polar coordinates the 100-lb pull vector to the right in the x direction would be written as 100 z 0 and the 150-lb pull vector to the upward y direction would be written as 150 z 90 . A rectangular coordinate vector representation is simply the x y location on graph paper of the tip of the vector arrow. A polar coordinate can be changed to a rectangular coordinate by the formula E z ộ Ecosộ j Esinộ For example the polar coordinate vector 100 z 0 can be written as 100 z 0 100cos0 j 100sin0 100 1 j 100 0 100 j 0 To draw this vector on a graph the tip of its arrow would be at 100 0 on cartesian graph paper and the base of the arrow would originate at 0 0 . Adding Vectors Vectors are added most easily in rectangular coordinate form. In this form each of the two parts of the coordinates is added together using simple algebra. For example to sum 80 z 60 80 z 135 as is shown in the solution of Fig. 3-1 the first thing that must be done is to hand sketch the vectors to .
