Vectors in the RC plane

Chapter Vectors in the RC plane

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • Vectors in the RC planeIf you work much with engineers, or if you plan to become one, you’ll get familiar withthe RC plane, just as you will with the RL plane. Recall from the last chapter that RL im-pedances can be represented as vectors. The same is true for RC impedances.In Fig. 14-6, there are four different impedance points. Each one is represented bya certain distance to the right of the origin (0,0), and a certain displacement down-wards. The first of these is the resistance, R, and the second is the capacitive reactance,Xc. Therefore, the RC impedance is a two-dimensional quantity.Doesn’t this look like a mirror-image reflection of RL impedances? You could almostimagine 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 RC plane can be rendered as vectors, just as this canbe done in the RL plane. Then the points become rays, each with a certain length anddirection. 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 distanceof the point from the origin, and the direction is the angle measured clockwise from theresistance (R) line, and specified in negative degrees. The equivalent vectors, for thepoints in Fig. 14-6, are illustrated in Fig. 14-7.Vectors in the RC plane25314-6Four points in the RC plane. See text for discussion.