Vectors in the RC Plane

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Four points in the RC plane.
Recall from the last topics that RL impedances can be represented as vectors. The same is true for RC impedances. In above figure, four different complex impedance points are shown. Each point is represented by a certain distance to the right of the origin (0,j 0), and a certain displacement downward. The first of these is the resistance, R, and the second is the capacitive reactance, XC. The complex RC impedance is a two-dimensional quantity.

Impedance points in the RC plane can be rendered as vectors, just as they can in the RL plane. Then the points become rays, each with a certain length and direction. The magnitude and direction for a vector, and the coordinates for the point, both uniquely define the same complex impedance. The length of the vector is the distance of the point from the origin, and the direction is the angle measured clockwise from the resistance (R) line, and specified in negative degrees. The equivalent vectors, for the points in above figure, are shown in following figure.

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