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7. Suppose a capacitor has X C = 8800 at f = 830 kHz. What is C (a) 2.18 F (b) 21.8 pF (c) 0.00218 F (d) 2.18 pF 8. Suppose a capacitor has C = 166 pF at f = 400 kHz. What is X C (a) 2.4 k (b) 2.4 (c) 2.4 10 6 (d) 2.4 M 9. Suppose a capacitor has C = 4700 F and XC = 33 . What is f (a) 1.0 Hz (b) 10 Hz (c) 1.0 kHz (d) 10 kHz 10. Each point in the RC plane (a) corresponds to a unique inductance. (b) corresponds to a unique capacitance. (c) corresponds to a unique combination of resistance and capacitance. (d) corresponds to a unique combination of resistance and reactance. 11. If R increases in an RC circuit, but X C is always zero, the vector in the RC plane will (a) rotate clockwise. (b) rotate counterclockwise. (c) always point straight toward the right. (d) always point straight down. 12. If the resistance R increases in an RC circuit, but the capacitance and the frequency are nonzero and constant, then the vector in the RC plane will (a) get longer and rotate clockwise. (b) get longer and rotate counterclockwise. (c) get shorter and rotate clockwise. (d) get shorter and rotate counterclockwise. 13. Each complex impedance value R jX C (a) represents a unique combination of resistance and capacitance. (b) represents a unique combination of resistance and reactance. (c) represents a unique combination of resistance and frequency. (d) All of the above are true.
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14. In an RC circuit, as the ratio XC /R approaches zero, the phase angle (a) approaches 90 . (b) approaches 0 . (c) stays the same. (d) cannot be found. 15. In a purely resistive circuit, the phase angle is (a) increasing. (b) decreasing. (c) 0 . (d) 90 . 16. If XC /R = 1, then what is the phase angle (a) 0 (b) 45 (c) 90 (d) Impossible to find because there s not enough data given 17. In Fig. 14-13, the impedance shown is (a) 8.02 + j323. (b) 323 + j8.02. (c) 8.02 j323. (d) 323 j8.02.
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Questions 17 and 18.
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18. In Fig. 14-13, note that the R and X C scale divisions are not the same size. What is the actual phase angle (a) 1.42 (b) About 60 , from the looks of it (c) 58.9 (d) 88.6 19. Suppose an RC circuit consists of a 150-pF capacitor and a 330- resistor in series. What is the phase angle at a frequency of 1.34 MHz (a) 67.4 (b) 22.6 (c) 24.4 (d) 65.6 20. Suppose an RC circuit has a capacitance of 0.015 F. The resistance is 52 . What is the phase angle at 90 kHz (a) 24 (b) 0.017 (c) 66 (d) None of the above
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CHAPTER
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Impedance and Admittance
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IN THIS CHAPTER, A COMPLETE, WORKING DEFINITION OF COMPLEX IMPEDANCE IS DEVELOPED. YOU LL
also get acquainted with admittance, the extent to which an ac circuit allows (or admits) current flow, rather than impeding it. As we develop these concepts, let s review, and then expand on, some of the material presented in the previous couple of chapters.
Imaginary Numbers
Have you been wondering what j actually means in expressions of impedance Well, j is nothing but a number: the positive square root of 1. There s a negative square root of 1, too, and it is equal to j. When either j or j is multiplied by itself, the result is 1. (Pure mathematicians often denote these same numbers as i or i.) The positive square root of 1 is known as the unit imaginary number. The set of imaginary numbers is composed of real-number multiples of j or j. Some examples are j4, j35.79, j25.76, and j25,000. The square of an imaginary number is always negative. Some people have trouble grasping this, but when you think long and hard about it, all numbers are abstractions. Imaginary numbers are no more imaginary (and no less real) than so-called real numbers such as 4, 35.79, 25.76, or 25,000. The unit imaginary number j can be multiplied by any real number on a conventional real number line. If you do this for all the real numbers on the real number line, you get an imaginary number line (Fig. 15-1). The imaginary number line should be oriented at a right angle to the real number line when you want to graphically portray real and imaginary numbers at the same time. In electronics, real numbers represent resistances. Imaginary numbers represent reactances.
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