Vectors in the RL Plane

Engineers sometimes represent points in the RL plane as vectors. Recall that a vector is a mathematical quantity that has a defined magnitude (length) and defined direction (orientation). Expressing a point in the RL plane as a vector thus gives that point a unique magnitude and a unique direction.

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above figure, four different points are shown. Each point is represented by a certain distance to the right of the origin (0,j0), and a certain distance upward from the origin. The first of these is the resistance, R, and the second is the inductive reactance, XL. Thus, the RL combination is a twodimensional quantity. There is no way to uniquely define RL combinations as single numbers, or scalars, because there are two different quantities that can vary independently.

Another way to depict these points is to draw lines from the origin out to them. Then you can think of the points as rays, each having a certain length, or magnitude, and a certain direction, or angle counterclockwise from the resistance axis. These rays, going out to the points, are complex impedance vectors (following figure)

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