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significant figures, is 89 . The circuit contains an almost pure inductive reactance, because the phase angle is close to 90 . The resistance contributes little to the behavior of this RL circuit at 1.0 MHz.
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Problem 13-6 What is the phase angle for the preceding circuit at a frequency of 10 kHz With that information, what can we say about the behavior of the circuit at 10 kHz This requires that XL be calculated again, for the new frequency. Let s use megahertz, so it goes in the formula with microhenrys. A frequency of 10 kHz is the same as 0.010 MHz. Calculating, we get XL = 6.28fL = 6.28 0.010 90 = 5.65 . The ratio XL/R is 5.65/10 = 0.565. Therefore, the phase angle is arctan 0.565, which, rounded to two significant figures, is 29 . This is not close to either 0 or 90 . Thus, at 10 kHz, the resistance and the inductive reactance both play significant roles in the behavior of the circuit.
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Refer to the text in this chapter if necessary. A good score is 18 correct. Answers are in the back of the book. 1. As the number of turns in a coil that carries ac increases without limit, the current in the coil will (a) eventually become very large. (b) stay the same. (c) decrease, approaching zero. (d) be stored in the core material. 2. As the number of turns in a coil increases, the reactance at a constant frequency (a) increases. (b) decreases. (c) stays the same. (d) is stored in the core material. 3. As the frequency of an ac wave gets lower, the value of XL for a particular coil of wire (a) increases. (b) decreases. (c) stays the same. (d) depends on the voltage. 4. Suppose a coil has an inductance of 100 mH. What is the reactance at a frequency of 1000 Hz (a) 0.628 (b) 6.28 (c) 62.8 (d) 628
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5. Suppose a coil shows an inductive reactance of 200 at 500 Hz. What is its inductance (a) 0.637 H (b) 628 H (c) 63.7 mH (d) 628 mH 6. Imagine a 400- H inductor with a reactance of 33 . What is the frequency (a) 13 kHz (b) 0.013 kHz (c) 83 kHz (d) 83 MHz 7. Suppose an inductor has XL = 555 at f = 132 kHz. What is L (a) 670 mH (b) 670 H (c) 460 mH (d) 460 H 8. Suppose a coil has L = 689 H at f = 990 kHz. What is XL (a) 682 (b) 4.28 (c) 4.28 k (d) 4.28 M 9. Suppose an inductor has L = 88 mH with XL = 100 . What is f (a) 55.3 kHz (b) 55.3 Hz (c) 181 kHz (d) 181 Hz 10. Each point in the RL plane (a) corresponds to a unique resistance. (b) corresponds to a unique inductance. (c) corresponds to a unique combination of resistance and inductive reactance. (d) corresponds to a unique combination of resistance and inductance. 11. If the resistance R and the inductive reactance XL both are allowed to vary from zero to unlimited values, but are always in the ratio 3:1, the points in the RL plane for all the resulting impedances will lie along (a) a vector pointing straight up. (b) a vector pointing east. (c) a circle. (d) a ray of indefinite length, pointing outward from the origin.
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12. Each specific complex impedance value defined in the form R + jXL (a) corresponds to a specific point in the RL plane. (b) corresponds to a specific inductive reactance. (c) corresponds to a specific resistance. (d) All of the above are true. 13. A vector is defined as a mathematical quantity that has (a) magnitude and direction. (b) resistance and inductance. (c) resistance and reactance. (d) inductance and reactance. 14. In an RL circuit, as the ratio of inductive reactance to resistance (XL/R) decreases, the phase angle (a) increases. (b) decreases. (c) stays the same. (d) becomes alternately positive and negative. 15. In a circuit containing inductive reactance but no resistance, the phase angle is (a) constantly increasing. (b) constantly decreasing. (c) equal to 0 . (d) equal to 90 . 16. If the inductive reactance and the resistance in an RL circuit are equal (as expressed in ohms), then what is the phase angle (a) 0 (b) 45 (c) 90 (d) It depends on the actual values of the resistance and the inductive reactance. 17. In Fig. 13-14, the impedance shown is which of the following (a) 8.0 (b) 90 (c) 90 + j8.0 (d) 8.0 + j90 18. Note that in the diagram of Fig. 13-14, the R and XL scale divisions are of different sizes. The phase angle can nevertheless be determined. It is (a) about 50 , from the looks of it. (b) 48 , as measured with a protractor.
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