Chapter 33. Alternating Current Circuits

Transcription

1 Chapter 33 Alternating Current Circuits Multiple Choice 1. An ac generator with peak voltage 100 volts is placed across a 10-Ω resistor. What is the average power dissipated? a. 100 W b. 150 W c. 500 W d W e W 2. An electric heater draws an average power of 1100 Watts when plugged into a 110 V-rms outlet. Calculate the resistance of the heater and the rms current. a. 11Ω, 10 A (rms) b. 110Ω, 10 A (rms) c. 10Ω, 11 A (rms) d. 10Ω, 110 A (rms) e..09ω, 11 A (rms) 3. An incandescent lightbulb is rated at 100 Watts when plugged into a 110 V-rms household outlet. Calculate the resistance of the filament and the rms current. a. 12.2Ω, 0.9A (rms) b. 10Ω, 1A (rms) c. 110Ω, 1A (rms) d. 122Ω, 0.9 A (rms) e. 11Ω, 1.1 A (rms) 4. A high-voltage powerline operates at 500,000 V-rms and carries an rms current of 500 A. If the resistance of the cable is.05ω/km, what is the resistive power loss in 200 km of the powerline? a. 250 kw b. 500 kw c. 1 Megawatt d. 2.5 Megawatts e. 250 Megawatts

2 2 Chapter A 230,000 V-rms powerline carries an average power P AV = 250 MW a distance of 200 km. If the total resistance of the cables is 10 ohms, what is the resistive power loss? a. 1.0 MW b. 2.5 MW c. 5.4 MW d MW e. 10 kw 6. Inductive reactance X L is given by a. Lω b. L/ω c. 1 /Lω d. ω/l e. ω 2 L 7. Capacitance reactance X C is given by a. 1/ωC b. ωc c. ω/c d. C/ω e. 1/ω 2 C 8. The total impedance Z of an RLC circuit driven by an ac voltage source at angular frequency ω is, a. R 2 + (ωl) 2 X C 2 b. R 2 + (X L X C ) 2 c. 1 R 2 + (X L X C ) 2 d. R 2 + (X L + X C ) 2 e. R 2 (X L + X C ) 2 9. At what frequency will a 12-µF capacitor have a reactance X C = 300Ω? a. 44 Hz b. 88 Hz c. 176 Hz d. 352 Hz e. 278 Hz 10. At what frequency will a 50-mH inductor have a reactance X L = 700Ω? a. 352 Hz b. 777 Hz c khz d khz e. 14 khz

3 Chapter A 2-µF capacitor in series with a 2-kΩ resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit. a ohms b ohms c ohms d ohms e ohms 12. A 10-µF capacitor is plugged into a 110 V-rms 60-Hz voltage source, with an ammeter in series. What is the rms value of the current through the capacitor? a A (rms) b A (rms) c A (rms) d A (rms) e A (rms) 13. A 0.5-H inductor is connected into a 110 V-rms 60-Hz voltage source, with an ammeter in series. What is the rms value of the current through the inductor? a A (rms) b A (rms) c A (rms) d A (rms) e A (rms) 14. An LC circuit is to have resonant oscillations at 5.0 MHz. Find the value of a capacitor which will work with a 1.0-mH inductor. a. 2 mf b. 1 µf c µf d. 1 pf e. 40 pf 15. The inductance of a tuning circuit of an AM radio is 4 mh. Find the capacitance of the circuit required for reception at 1200 khz. a. 2.1 pf b. 4.4 pf c pf d pf e pf 16. Find the resonant frequency for a series RLC circuit where R = 10Ω, C = 5 µf, and L = 2 mh. a. 998 Hz b khz c khz d khz e khz

4 4 Chapter The voltage 8 sin (400t) is applied to a series RLC circuit, with R = 200Ω, L = 0.1 H, and C = 1 µf. What are the impedance Z and the phase angle θ? a. 200 Ω, 37 b. 566 Ω, +87 c Ω, 85.4 d Ω, 88.8 e. 393 Ω, If an R = 1-kΩ resistor, a C = 1-µF capacitor, and an L = 0.2-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source? a A b. 27 ma c. 54 ma d A e A 19. If the input to an RLC series circuit is V = V m cos ωt, then the current in the circuit is a. b. c. d. V m cos ωt R V m cos ωt R 2 + ω 2 L 2 V m sin ωt R 2 + (ωl + 1/ωC) 2 V m cos (ωt φ) R 2 + (ωl 1/ωC) 2 e. V m R ωl cos ωt ωc 20. An RLC series circuit has R = 100 ohms, C = 25 µf, and L =.16 H. For what angular frequency of an ac voltage is the current flow maximum? a. 251 rad/s b. 500 rad/s c. 757 rad/s d. 884 rad/s e rad/s

5 Chapter Determine the rms voltage for the circuit. 1 kω V = 140 sin (500 t) 1 Η 1 µf a. 99 V (rms) b. 140 V (rms) c. 196 V (rms) d. 70 V (rms) e. 110 V (rms) 22. Determine the impedance for the circuit. 1 kω V = 140 sin (500 t) 1 Η 1 µf a. 600 Ω b Ω c Ω d Ω e Ω 23. Determine the rms current for the circuit. 1 kω V = 140 sin (500 t) 1 Η 1 µf a. 55 ma b. 77 ma c. 99 ma d A e. 61 ma

6 6 Chapter Determine the resonant frequency of the circuit. 1 kω V = 140 sin (500 t) 1 Η 1 µf a. 159 Hz b. 32 Hz c. 5 Hz d. 500 Hz e Hz 25. Determine the rms voltage drop across the resistor in the circuit. 1 kω V = 140 sin (500 t) 1 Η 1 µf a. 55 V b. 77 V c. 9.9 V d. 5.5 V e. 61 V 26. Determine the rms voltage drop across the inductor in the circuit. 1 kω V = 140 sin (500 t) 1 Η 1 µf a. 11 V b V c. 33 V d V e V

7 Chapter Determine the rms voltage drop across the capacitor in the circuit. 1 kω V = 140 sin (500 t) 1 Η 1 µf a. 55 V b. 77 V c. 110 V d. 154 V e. 198 V 28. A current I = 3 sin (400 t) amperes flows in a series RL circuit in which L = 1 mh and R = 100Ω. What is the average power loss? a. 225 W b. 450 W c. 980 W d kw e. 900 W 29. What is the average power dissipation in a series RC circuit if R = 5 kω, C = 2 µf, and V = 170 cos (300t)? a W b W c W d. 157 W e W 30. What is the average power dissipation in an RLC series circuit with R = 10Ω, L = 0.1 H, C = 10 µf when driven at resonance by a 100 V-rms source? a. 100 W b. 500 W c W d. 2 kw e. 700 W 31. A series RLC circuit has an impedance of 120Ω and a resistance of 64Ω. What average power is delivered to this circuit when V rms = 90 volts? a. 36 W b. 100 W c. 192 W d. 360 W e. 12 W

8 8 Chapter A transformer is to be designed to increase the 30 kv-rms output of a generator to the transmission-line voltage of 345 kv-rms. If the primary winding has 80 turns, how many turns must the secondary have? a. 6 b. 70 c. 920 d e The primary winding of an electric train transformer has 400 turns and the secondary has 50. If the input voltage is 120V(rms) what is the output voltage? a. 15 V (rms) b. 30 V (rms) c. 60 V (rms) d. 2.4 V (rms) e. 960 V (rms) 34. A step-up transformer has an input voltage of 110V(rms). There are 100 turns on the primary and 1500 on the secondary. What is the output voltage? a V (max) b V (rms) c V (max) d. 165 kv (rms) e. 7.3 V (rms) 35. A primary current of 6 A exists in an ideal iron-core transformer at a primary voltage of 100 volts. If the current in the secondary is.75 A, calculate the output voltage. a V b. 40 V c. 400 V d. 800 V e. 200 V 36. An ideal step-down transformer has 200 primary turns and 50 secondary turns. If 440 volts (rms) is placed across the primary, what is the current in the secondary if the load resistance is 7 ohms? a. 3.6 A (rms) b. 7.3 A (rms) c A (rms) d A (rms) e A (rms)

9 Chapter Calculate V out /V in for the circuit if R = 2 kω, C = 0.02 µf and V = 140V sin(50,000t) R V in C Vout a b c. 0.8 d e The impedance of the parallel RLC circuit shown is given by V 0 sin ωt R L C a. b. c. 1 R + 1 ωl + ωc 1 R 2 + ωc 1 ωl 1 R + 1 ωl 1 ωc 2 1/2 d. R ωl ωc e. 1 R 2 + ωc 1 ωl 39. The rms current from the voltage source is 2 V 0 sin ωt R L C a. V rms Z b. V rms /Z c. V rms /R d. V rms /(R +X L X C ) e. V rms /(2Z)

10 10 Chapter The phase angle between V and I is V 0 sin ωt R L C a. tan 1 R R X C X L b. tan 1 R X C X L c. tan 1 X C X L R d. tan 1 R R 2 + (X L X C ) 2 e. tan 1 R 2 + (X L X C ) For driving voltage V = V m sin t, the current through the resistor is V 0 sin ωt R L C a. V m sin (ωt + φ) b. V m cos (ωt + φ) c. d. e. V m R V m sin (ωt + φ) sin (ωt + φ) Z V m sin ωt R 42. If R = 10 ohms, L = 0.1 henry, C = 10 µf, what is the resonant frequency for the parallel RLC-circuit? a Hz b. 333 Hz c. 159 Hz d. 53 Hz e. 500 Hz Conceptual Problems 43. Suppose the circuit parameters in a series RLC circuit are: L = 1.0 µh, C = 10.0 nf, R = 100Ω, and the source voltage is 22 V. Determine the resonant frequency of the circuit and the amplitude of the current at resonance.

11 Chapter A 10-Ω resistor, 10-mH inductor, and 10-µF capacitor are connected in series with a 10-kHz voltage source. The rms current through the circuit is 0.20 A. Find the voltage drop across each of the 3 elements. 45. An ac power generator produces 50 A (rms) at 3600 V. The voltage is stepped up to 100,000 V by an ideal transformer and the energy is transmitted through a long distance power line which has a resistance of 100 ohms. What percentage of the power delivered by the generator is dissipated as heat in the long-distance power line? 46. An alternating current circuit has resistance R, inductance L and capacitance C in series with a voltage source. Which statement is correct? a. The voltage across the capacitor leads the voltage across the inductor by 90. b. The voltage across the inductor leads the voltage across the capacitor by 90. c. The voltage across the capacitor leads the voltage across the inductor by 180. d. The voltage across the inductor leads the voltage across the capacitor by 180. e. Both voltages lead the voltage across the resistor by In a series ac LRC circuit a. capacitors and inductors act as short circuits at high frequencies. b. capacitors and inductors act as open circuits at low frequencies. c. a capacitor acts as an open circuit at low frequencies and as a short circuit at high frequencies. d. an inductor acts as an open circuit at low frequencies and as a short circuit at high frequencies. e. a capacitor acts as a short circuit at high frequencies and an inductor acts as a short circuit at low frequencies. 48. The power output, Pout, of a step-up transformer that receives power input, Pin, and which has N1turns in the primary and N2 turns in the secondary coil is given by a. P out = P in b. P out = N 2 N 1 P in. c. P out = N 1 P N in. 2 d. P out = N 2 N 1 e. P out = N 1 N 2 2 Pin. 2 Pin. 49. In a typical transmission line, the current I is very small and the voltage V is very large. A unit length of line has resistance R. For a power line that supplies power to 10,000 households, we can conclude that a. IV = I 2 R. b. I = V/R. c. IV<I 2 R. d. IV>I 2 R. e. I 2 R = 0.

12 12 Chapter Whenever the alternating current frequency in a series RLC circuit is halved, a. the inductive reactance is doubled and the capacitive reactance is halved. b. the inductive reactance is doubled and the capacitive reactance is doubled. c. the inductive reactance is halved and the capacitive reactance is halved. d. the inductive reactance is halved and the capacitive reactance is doubled. e. the reactance of the circuit remains the same. 51. The average power input to a series alternating current circuit is minimum when a. there are only a resistor and capacitor in the circuit. b. there are only a resistor and inductor in the circuit. c. there is only a resistor in the circuit d. X L = X C and the circuit contains a resistor, an inductor and a capacitor. e. there is only a capacitor in the circuit.

13 Chapter 33 1 Chapter 33 Alternating Current Circuits 1. Answer: c 2. Answer: a 3. Answer: d 4. Answer: d 5. Answer: d 6. Answer: a 7. Answer: a 8. Answer: b 9. Answer: a 10. Answer: d 11. Answer: d 12. Answer: b 13. Answer: c 14. Answer: d 15. Answer: b 16. Answer: b 17. Answer: c 18. Answer: c 19. Answer: d 20. Answer: b 21. Answer: a 22. Answer: c 23. Answer: a

14 2 Chapter Answer: a 25. Answer: a 26. Answer: b 27. Answer: c 28. Answer: b 29. Answer: b 30. Answer: c 31. Answer: a 32. Answer: c 33. Answer: a 34. Answer: b 35. Answer: d 36. Answer: d 37. Answer: b 38. Answer: b 39. Answer: b 40. Answer: a 41. Answer: e 42. Answer: c 43. Answer: 1.59 MHz, 0.22 A 44. Answer: 2.0 V, V, V 45. Answer: 0.18% 46. Answer: d 47. Answer: e 48. Answer: a 49. Answer: d

15 Chapter Answer: d 51. Answer: e

16 4 Chapter 33