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244 Impedance and Admittance
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14. An inductor has a value of 44 mH at 60 Hz. What is the inductive susceptance, stated as an imaginary number (a) BL = j0.060 (b) BL = j0.060 (c) BL = j17 (d) BL = j17 15. Susceptance and conductance add to form (a) complex impedance. (b) complex inductance. (c) complex reactance. (d) complex admittance. 16. Absolute-value impedance is equal to the square root of which of the following (a) G 2 + B 2 (b) R 2 + X 2 (c) Zo (d) Y 2 + R 2 17. Inductive susceptance is defined in (a) imaginary ohms. (b) imaginary henrys. (c) imaginary farads. (d) imaginary siemens. 18. Capacitive susceptance values can be defined by (a) positive real numbers. (b) negative real numbers. (c) positive imaginary numbers. (d) negative imaginary numbers. 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, as the absolute value of the impedance in a circuit increases, (a) the flow of ac increases. (b) the flow of ac decreases. (c) the reactance decreases. (d) the resistance decreases.
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CHAPTER
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WHEN YOU SEE AN AC CIRCUIT THAT CONTAINS COILS AND/OR CAPACITORS, YOU SHOULD ENVISION a complex-number plane, either RX (resistance-reactance) or GB (conductance-admittance). The RX plane applies to series circuit analysis. The GB plane applies to parallel circuit analysis.
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Complex Impedances in Series
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When you see resistors, coils, and capacitors in series, each component has an impedance that can be represented as a vector in the RX plane. The vectors for resistors are constant, regardless of the frequency. But the vectors for coils and capacitors vary with frequency.
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Pure Reactances Pure inductive reactances (X L ) and capacitive reactances (X C ) simply add together when coils and capacitors are in series. Thus, X = X L + X C. In the RX plane, their vectors add, but because these vectors point in exactly opposite directions inductive reactance upward and capacitive reactance downward (Fig. 16-1) the resultant sum vector inevitably points either straight up or straight down, unless the reactances are equal and opposite, in which case they cancel and the result is the zero vector. Problem 16-1 Suppose a coil and capacitor are connected in series, with jX L = j200 and jX C = j150. What is the net reactance Just add the values: jX = jX L + jX C = j200 + ( j150) = j(200 150) = j50. This is a pure inductive reactance, because it is positive imaginary. Problem 16-2 Suppose a coil and capacitor are connected in series, with jXL = j30 and jX C = j110. What is the net reactance
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246 RLC and GLC Circuit Analysis
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16-1 Pure inductance and
pure capacitance are represented by reactance vectors that point straight up and down.
Again, add the values: jX = j30 + ( j110) = j(30 110) = j80. This is a pure capacitive reactance, because it is negative imaginary.
Problem 16-3 Suppose a coil of inductance L = 5.00 H and a capacitor of capacitance C = 200 pF are connected in series. Suppose the frequency is f = 4.00 MHz. What is the net reactance First, calculate the reactance of the inductor at 4.00 MHz. Proceed as follows:
jXL = j6.28f L = j(6.28 4.00 5.00) = j126 Next, calculate the reactance of the capacitor at 4.00 MHz. Proceed as follows: jX C = j[1/(6.28f C )] = j[1/(6.28 4.00 0.000200)] = j199 Finally, add the inductive and capacitive reactances to obtain the net reactance: jX = jXL + jX C = j126 + ( j199) = j 73 This is a pure capacitive reactance.
Problem 16-4 What is the net reactance of the aforementioned inductor and capacitor combination at the frequency f = 10.0 MHz
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