AP Physics C Alternating Current Chapter Problems Sources of Alternating EMF 1. A 10 cm diameter loop of wire is oriented perpendicular to a 2.5 T magnetic field. What is the magnetic flux through the loop? 2. A circular loop of wire with a radius of 15 cm is placed in a perpendicular magnetic field with a magnitude of 1.6 T. What is the magnetic flux through the loop? 3. A rectangular loop of wire with dimensions of 15x20 cm is placed in a uniform magnetic field of magnitude 1.8 T. The angle between the magnetic field and the normal to the loop is 30. What is the magnetic flux through the loop? 4. A rectangular loop of wire with dimensions of 12x30 cm is placed in a uniform magnetic field of magnitude 1.4 T. The angle between the magnetic field and the normal to the loop is 60. What is the magnetic flux through the loop? 5. A flux of 2x10-5 Wb is maintained through a circular loop of wire with a radius of 10 cm. The loop is oriented perpendicular to the magnetic field. What is the magnitude of the magnetic field? 6. A flux of 5x10-4 Wb is maintained through a rectangular loop of wire with dimensions of 25x40 cm. The loop is oriented perpendicular to the magnetic field. What is the magnitude of the magnetic field? 7. The magnetic flux through a coil of wire containing 100 loops changes from 25 Wb to 75 Wb in 0.05 s. What is the induced emf in the coil? 8. The magnetic flux through a coil of wire containing 200 loops changes from -20 Wb to 80 Wb in 0.04 s. What is the induced emf in the coil? 9. The magnetic field perpendicular to a circular loop of wire with a radius of 18 cm is changed from 0.5 T to 2.5 T in 0.02 s. Calculate the induced emf in the loop. 10. The magnetic field perpendicular to a circular loop of wire with a radius of 25 cm is changed from 0.2 T to 1.8 T in 0.15 s. Calculate the induced emf in the loop. 11. A 30 cm diameter loop of wire is initially oriented perpendicular to a 2.4 T magnetic field. The loop is rotated around its diameter so that is parallel to the filed direction in 0.3 s. What is the induced emf in the loop? 12. A 25 cm diameter loop of wire is initially oriented parallel to a 3.2 T magnetic field. The loop is rotated around its diameter so that is perpendicular to the filed direction in 0.15 s. What is the induced emf in the loop? 13. An AC generator consists of 200 turns of wire of area 0.08 m2. The loops rotate in a magnetic field of 0.4 T at a constant angular speed of 50 revolutions per second. Find the maximum induced emf.
14. An AC generator consists of 150 turns of wire of area 0.07 m2. The loops rotate in a magnetic field of 0.4 T at a constant angular speed of 60 revolutions per second. Find the maximum induced emf. 15. An AC generator consists of 400 turns of wire of area 0.06 m2 and total resistance of 15 Ω. The loops rotate in a magnetic field of 0.5 T at a constant angular speed of 50 revolutions per second. Find the maximum induced current. 16. An AC generator consists of 200 turns of wire of area 0.09 m2 and total resistance of 10 Ω. The loops rotate in a magnetic field of 0.6 T at a constant angular speed of 60 revolutions per second. Find the maximum induced current. 17. An AC generator produces a maximum voltage of 9 V when rotated at a constant rate of 375 rad/s in a uniform magnetic field of 0.05 T. The rotating area of the coil is 200 cm 2. How many loops are in the coil? 18. An AC generator with 200 loops produces a maximum voltage of 12 V when rotated at a constant rate in a uniform magnetic field of 0.05 T. The rotating area of the coil is 200 cm 2. What is the rotating frequency of the coil? Transformers 19. A step-up transformer changes voltage from 120 V to 12,000 V. There are 500 turns in the primary coil. How many turns are in the secondary coil? 20. A step-up transformer changes voltage from 12 V to 120 V. There are 400 turns in the secondary coil. How many turns are in the primary coil? 21. A transformer has 48 turns in the primary coil and 240 turns in the secondary coil. What voltage is present in the secondary coil if 9 V is applied to the primary coil? 22. A transformer has 150 turns in the primary coil and 900 turns in the secondary coil. What voltage is present in the primary coil if 54 V is measured at the secondary coil? 23. A transformer has 400 turns in the primary coil and 1600 turns in the secondary coil. If the current in the secondary is 1.5 A, what is the current in the primary? 24. A transformer has 3000 turns in the primary coil and 150 turns in the secondary coil. If the current in the primary is 5 A, what is the current in the secondary? AC Circuits and Impedance 25. Voltage across the terminals of an ac power supply varies with time according the following: V = 45 cos(πt). What is the rms voltage? 26. An ac current varies with time according the following: I = 2 cos(2πt). What is the rms current? 27. A 5000 Ω resistor is connected to an ac circuit with I rms = 0.4 A. What is the average power dissipated in the resistor? 28. A 4000 Ω resistor is connected to an ac circuit with V rms = 110 V. What is the average power dissipated in the resistor? 29. What is the reactance of a 4 H inductor at a frequency of 60 Hz? 30. What is the reactance of a 6 H inductor at a frequency of 80 Hz? 31. What is the reactance of a 4 µf capacitor at a frequency of 60 Hz? 32. What is the reactance of a 6 µf capacitor at a frequency of 80 Hz?
33. A 150 mh inductor has a reactance of 3 kω. Calculate the frequency of an ac current? 34. A 9 µf capacitor has a reactance of 360 Ω. Calculate the frequency of an ac current? LRC Circuits 35. A 25 kω resistor is connected in series with a 0.4 H inductor and an ac source. Calculate the impedance of the circuit if the frequency of the source is 60 Hz. 36. A 4 kω resistor is connected in series with a 5 µf capacitor and an ac source. Find the impedance of the circuit if the source frequency is 100 Hz. 37. A 250 Ω resistor, a 0.4 H inductor, and a 5 µf capacitor are connected in series with each other and an ac power supply operating at a frequency of 60 Hz. Calculate the impedance of the circuit. 38. A 500 Ω resistor, a 0.6 H inductor, and a 4 µf capacitor are connected in series with each other and an ac power supply operating at a frequency of 100 Hz. Calculate the impedance of the circuit. 39. An LRC circuit is connected to a1000 Hz power supply operating with rms voltage of 240 V. Calculate the phase angle if L=0.02 H, R=10 kω, and C=5 µf. 40. An LRC circuit is connected to a 500 Hz power supply operating with rms voltage of 120 V. Calculate the phase angle if L=0.04 H, R=5 kω, and C=2 µf. Resonance 41. A 4 µf capacitor is connected to a 0.05 mh inductor. What is the resonance frequency? 42. A 5 µf capacitor is connected to a 0.04 mh inductor. What is the resonance frequency? 43. An ac circuit containing a 2 µf capacitor and an inductor oscillates at a frequency of 10 khz. Calculate the inductance. 44. An ac circuit containing a 3 µf capacitor and an inductor oscillates at a frequency of 5 khz. Calculate the inductance. 45. An ac circuit containing a 0.08 mh inductor and a capacitor oscillates at a frequency of 5 khz. Calculate the capacitance. 46. An ac circuit containing a 0.09 mh inductor and a capacitor oscillates at a frequency of 12 khz. Calculate the capacitance.
Free Response Problems 1. A circular loop of wire with a radius of 20 cm and resistance of 2.5 Ω is placed perpendicular to a uniform magnetic field. The magnetic field changes from 0.4 T to 3.2 T in 0.3 s. a. Calculate the induced emf in the loop. b. Indicate the direction of the induced current. c. Calculate the induced current in the loop. d. Calculate the rate of thermal energy that is produced in the loop. 2. A simple generator has a square armature with 1000 loops that are 15 cm on a side. The armature rotates in a field of 0.5 T at a rate of 60 rev/s. The total resistance is 25 Ω. a. Find the maximum induced emf. b. Find the maximum induced current. c. What would you do to the generator in order to increase the maximum emf? 3. A 500 loop circular armature coil with a radius of 15 cm rotates at a rate of 60 rev/s in a uniform magnetic field of 1.75 T. The total resistance is 45 Ω. a. Calculate the maximum induced emf. b. Calculate the rms voltage output of the generator. c. Calculate the rms current. d. How would you change the rotational frequency in order to double the rms voltage output? 4. A desk lamp is design to operate at 40 W when connected to 12 V ac power supply. A transformer is needed to convert 120 V household voltage. a. Is the transformer step-up or step-down? b. What is the current in the secondary coil when the lamp is on? c. What is the current in the primary coil when the lamp is on? d. What is the resistance of the bulb? 5. A transformer is connected to 120 V (rms) ac power line supplies a 12,000 V for an X-ray tube. The current in the secondary coil is 0.5 ma. a. What is the ratio of secondary to primary turns of the transformer? b. What power must be supply to the transformer? c. What is the current in the primary coil?
6. An LRC series circuit is connected to 120 V (rms) and 60 Hz ac power supply. In the circuit R =200 Ω, L=2 H, and C =0.5 µf. d. Find the phase angle between voltage and current. e. Find the power dissipated in the circuit. 7. An LRC series circuit consists of a 20 mh inductor, a 8 kω resistor, and a 5 µf capacitor. The circuit is connected to 10 khz, 340 V (rms) ac source. d. Find the phase angle between voltage and current. e. Find the power dissipated in the circuit. 8. An LRC series circuit is connected to 120 V (rms) and 60 Hz ac power supply. In the circuit R =200 Ω, L=2 H, and C =0.5 µf. d. Find the maximum value of voltage across R. e. Find the maximum value of voltage across L. f. Find the maximum value of voltage across C. g. Compare your result form (a) and the sum from (d), (e), (f). h. For what value of ω is V L=V C? What is the significance of this value?