Ch3 - 58 Chapter 3 Alternating Current Circuits I 3-6...

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Unformatted text preview: 58 Chapter 3 Alternating Current Circuits I 3-6 QUESTIONS AND PROBLEMS 1. Complete the following summary table. Resistance Capacitance general v-i di relationship dt dc relationship I = 0 resistance or R reactance impedance R + j0 v-i vector — j relationship 19C 2. A sine wave signal (20 V PP) is connected to a 10 k0 A resistor. Calculate the current through the resistor in terms of average, rms, and peak currents. What wattage rating should the resistor have? 3. Determine the relationships among VP, me and VPP for a square wave of amplitude i VP. 4. Determine the relationships among VP, VW, and VPP for a triangular wave of amplitude : VP, for which the de— scription between 0 and ’lT/2 is v = 7% tot. ’IT 5. Compare the rms currents and power dissipations that would occur if the waveforms of problems 2, 3 and 4 were applied in turn to a 10 k0 resistor; in all cases, VPP= 20 V. 6. Calculate the magnitude and phase angle of the imped- ance for the circuit of Figure A. lOkQ 150 Hz 0.2 uF FIGURE A Circuit for problems 6, 7, 8, 9 and 10. 7. At what frequency will the phase angle be 30° for the circuit of Figure A? 8. Using the circuit values of Figure A, plot vow/vin (where Vom is taken across the capacitor) versus the log of frequency. Also plot the log of vent/vin versus the log of frequency. 9. Again using the circuit values of Figure A, make the same plots as in problem 8, but taking vout across the resistor. 10. With reference to the plots of problems 8 and 9, is there a frequency at which vow/v,n is the same in both cases? Explain. 11. Determine the resonance frequency for the series cir- cuit of Figure B. HH—ar—o 2 ”F 1 k9 FIGURE B Circuit for problems 11 and 12. 12. Calculate the magnitude and phase angle of the impedance of the circuit in Figure B when it is operated at 2500 Hz. 13. What value of L is necessary for resonance at 10,000 Hz for the circuit of Figure C when R = 570 .Q and C = 0.01 uF? 14. Given that L = 0.05 H in the circuit of Figure C, and the values of R and C as in problem 13, calculate the phase angle and magnitude of the impedance of the circuit at 100 kHz. 15. For the R, L and C values in problem 14, what are the Q values of the circuit of Figure C at 100 kHz, 1000 Hz, and 100 Hz? FIGURE C Circuit for problems 13, 14 and 15. 16. For the high-pass filter of Figure D, at what frequency is v /vin : 0.95? out 17. At what frequencies will the circuit of Figure D act as a differentiator? o—I 0'1“}: 10m FIGURE D Circuit for problems 16, 17, 18 and 19. 18. Interchanging R and C of Figure D produces a low- pass filter. At what frequency will vent/Vin = 0.95? 19. At what frequencies will the RC circuit of problem 18 2‘; act as an integrator? 20. Design a low—pass filter that has vow/vin = 0.5 at 1 5 kHz. _ 21. For the circuit that you designed in problem 20, at f what frequencies will vow/vin equal 0.01 and 0.99? : 22. Consider an RLC series circuit in which R = 1 k0, L = 1 H and C = 0.1 uF. calculate the resonance frequency, ‘A the impedance at resonance and the current at resonance } when Vrms = 10 V. Also sketch XL, XC, d) and Z as functions 2 of frequency. : 23. Consider an RLC parallel circuit, as in Figure C, in Q which the component values are R = 1 k0, C = 0.1 uF, 24. Derive the following gain expression for the circuit of L Figure B: Y.» ____Rfi__ vs R2+R1 (1 +ooCR2) FIGURE E Circuit for problems 24 and 25. Under what frequency conditions will the circuit of Figure E behave as a simple voltage divider? and L = l H. Sketch Z, In,” and (l) as functions of frequency. Chapter 3 Alternating Current Circuits I 59 26. Derive the following gain expression for the circuit of Figure F: FIGURE F Circuit for problems 26, 27 and 28. 27. Under what conditions of R and C will the gain of the circuit of Figure F be the same as that of a simple voltage divider? 28. Suggest a possible use for the circuit of Figure F. 29. Consider the circuit of Figure G, where R1 -= 20 0, X1 = 37.7 (1, R2 = 10 Q, and X2 = —53.1 9. Compute the current and the phase angle between the current and the applied voltage. 30. Determine the values of L and C used in problem 29. FIGURE G Circuit for problems 29 and 30. ...
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