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Complex admittances can be shown as vectors, just as can complex impedances. In Fig. 15-10, the points from Fig. 15-9 are rendered as vectors. Generally, longer vectors indicate greater flow of current, and shorter ones indicate less current. Imagine a point moving around on the GB plane, and think of the vector getting longer and shorter, and changing direction. Vectors pointing generally northeast, or upwards and to the right, correspond to conductances and capacitances in parallel. Vectors pointing in a more or less southeasterly direction, or downwards and to the right, are conductances and inductances in parallel.
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Why all these different expressions
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Do you think that the foregoing discussions are an elaborate mental gymnastics routine Why do you need all these different quantities: resistance, capacitance, capacitive reactance, inductance, inductive reactance, impedance, conductance, capacitive susceptance, inductive susceptance, admittance Well, gymnastics are sometimes necessary to develop skill. Sometimes you need to break a mental sweat. Each of these expressions is important. The quantities that were dealt with before this chapter, and also early in this chapter, are of use mainly with series RLC (resistance-inductance-capacitance) circuits. The ones introduced in the second half of this chapter are important when you need to analyze parallel RLC circuits. Practice them and play with them, especially if they intimidate you. After awhile they ll become familiar.
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15-10 Vectors representing the points of Fig. 15-9.
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Think in two dimensions. Draw your own RX and GB planes. (Be thankful there are only two dimensions, and not three! Some scientists need to deal in dozens of dimensions.) If you want to be an engineer, you ll need to know how to handle these expressions. If you plan to manage engineers, you ll want to know what these quantities are, at least, when the engineers talk about them. If the math seems a bit thick right now, hang in there. Impedance and admittance are the most mathematical subjects you ll have to deal with.
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Refer to the text in this chapter if necessary. A good score is 18 or more correct. Answers are in the back of the book. 1. The square of an imaginary number: A. Can never be negative.
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Quiz 281 B. Can never be positive. C. Might be either positive or negative. D. Is equal to j. 2. A complex number: A. Is the same thing as an imaginary number. B. Has a real part and an imaginary part. C. Is one-dimensional. D. Is a concept reserved for elite imaginations. 3. What is the sum of 3 A. 0 j0 B. 6 j14. C. 6 j14. D. 0 j14. j7) (4 j5) 4. What is ( 5 A. 1 j2. B. 9 j2. C. 1 j2. D. 9 j12. j7 and 3 j7
5. What is the product ( 4 A. 24 j14. B. 38 j34. C. 24 j14. D. 24 j14.
j7)(6
j2)
6. What is the magnitude of the vector 18 A. 42. B. 42. C. 30. D. 30.
j24
7. The impedance vector 5 j0 represents: A. A pure resistance. B. A pure inductance. C. A pure capacitance. D. An inductance combined with a capacitance. 8. The impedance vector 0 A. A pure resistance. B. A pure inductance. j22 represents:
282 Impedance and admittance C. A pure capacitance. D. An inductance combined with a resistance. 9. What is the absolute-value impedance of 3.0 A. Z B. Z C. Z D. Z A. Z B. Z C. Z D. Z 9.0 . 3.0 . 45 . 6.7 . j235 240 . 58,000 . 285 . 185 . j6.0
10. What is the absolute-value impedance of 50
11. If the center conductor of a coaxial cable is made to have smaller diameter, all other things being equal, what will happen to the Zo of the transmission line A. It will increase. B. It will decrease. C. It will stay the same. D. There is no way to know. 12. If a device is said to have an impedance of Z 100 , this would most often mean that: A. R jX 100 j0. B. R jX 0 j100. C. R jX 0 j100. D. You need to know more specific information. 13. A capacitor has a value of 0.050 F at 665 kHz. What is the capacitive susceptance A. j4.79. B. j4.79. C. j0. 209. D. j0. 209. 14. An inductor has a value of 44 mH at 60 Hz. What is the inductive susceptance A.. j0.060. B. j0.060. C. j17. D. j17.
Ions 283 15. Susceptance and conductance add to form: A. Impedance. B. Inductance. C. Reactance. D. Admittance. 16. Absolute-value impedance is equal to the square root of: A. G2 B2 B. R2 C. Zo. D. Y. 17. Inductive susceptance is measured in: A. Ohms. B. Henrys. C. Farads. D. Siemens. 18. Capacitive susceptance is: A. Positive and real valued. B. Negative and real valued. C. Positive and imaginary. D. Negative and imaginary. 19. Which of the following is false A. BC 1/XC. B. Complex impedance can be depicted as a vector. C. Characteristic impedance is complex. D. G 1/R. 20. In general, the greater the absolute value of the impedance in a circuit: A. The greater the flow of alternating current. B. The less the flow of alternating current. C. The larger the reactance. D. The larger the resistance. X2.