Vectors in the RC plane

If you work much with engineers, or if you plan to become one, you’ll get familiar with the RC plane, just as you will with the RL plane. Recall from the last chapter that RL impedances can be represented as vectors. The same is true for R_C impedances.
There are four different impedance points. Each one is represented by a certain distance to the right of the origin (0,0), and a certain displacement downwards. The first of these is the resistance, R, and the second is the capacitive reactance, Xc. Therefore, the R_C impedance is a two-dimensional quantity.
Doesn’t this look like a mirror-image reflection of RL impedances? You could almost imagine that we’re looking at an RL plane reflected in a pool of still water. This is, in fact, an excellent way to envision this situation.
The impedance points in the R_C plane can be rendered as vectors, just as this can be done 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 impedance value. 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, are illustrated in Fig. 1.

Fig. 1 Four vectors in the RC impedance plane.