Induction. d. is biggest when the motor turns fastest.

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1 Induction 1. A uniform 4.5-T magnetic field passes perpendicularly through the plane of a wire loop 0.10 m 2 in area. What flux passes through the loop? a. 5.0 T m 2 c T m 2 b T m 2 d T m 2 2. According to Lenz s law the direction of an induced current in a conductor will be that which tends to produce which of the following effects? a. enhance the effect which produces it c. produce the greatest voltage b. produce a greater heating effect d. oppose the effect which produces it 3. The back emf of a motor refers to a source of voltage that: a. occurs when the motor runs backwards. c. is biggest when the current through the motor is biggest. b. occurs when the motor is used as a generator. d. is biggest when the motor turns fastest. 4. When a voltage is generated by rotating a coil in a magnetic field at a constant rate, the period of the voltage equals the time that it takes for the coil to rotate through radians. a. 1 c. b. /2 d An inductor, battery, resistance, and ammeter and switch are connected in series. If the switch, initially open, is now closed, what is the current s final value? a. zero c. battery voltage times inductance b. battery voltage divided by inductance d. battery voltage divided by resistance 6. In a circuit made up of inductor, resistance, ammeter, battery and switch in series, at which of the following times after the switch is closed is the rate of current increase greatest? a. zero c. reciprocal of one time constant b. one time constant d. ten time constants 7. How is the energy stored in a current-carrying inductor related to its self-inductance, L? a. directly proportional to L 2 c. directly proportional to L b. directly proportional to L 1/2 d. inversely proportional to L 8. How is the energy stored in a current-carrying inductor related to the current value, I? a. directly proportional to I 2 c. directly proportional to I b. directly proportional to I 1/2 d. inversely proportional to I 9. A uniform 4.5-T magnetic field passes through the plane of a wire loop 0.10 m 2 in area. What flux passes through the loop when the direction of the 4.5-T field is at a 30 angle to the normal of the loop plane? a. 5.0 T m 2 c T m 2 b T m 2 d T m 2 1

2 10. A square coil, enclosing an area with sides 2.0 cm long, is wrapped with turns of wire. A uniform magnetic field perpendicular to its plane is turned on and increases to 0.25 T during an interval of 1.0 s. What average voltage is induced in the coil? a V c. 2.0 V b V d. 2.5 V 11. A 10-turn square coil of area m 2 and a 20-turn circular coil are both placed perpendicular to the same changing magnetic field. The voltage induced in each of the coils is the same. What is the area of the circular coil? a m 2 c m 2 b m 2 d m A flat coil of wire consisting of 20 turns, each with an area of 50 cm 2, is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s. If the coil has a total resistance of 0.40, what is the magnitude of the induced current? a. 70 ma c. 500 ma b. 140 ma d. 800 ma 13. A planar loop consisting of four turns of wire, each of which encloses 200 cm 2, is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mt to 25 mt in a time of 5.0 ms. What is the resulting induced current in the coil if the resistance of the coil is 5.0? a. 60 ma c ma b. 12 ma d. 48 ma 14. A m wire is moved parallel to a T magnetic field at a speed of 1.50 m/s. What emf is induced across the ends of the wire? a V c V b V d. zero 15. An airplane with a wingspan of 60.0 m flies parallel to the Earth s surface at a point where the downward component of the Earth's magnetic field is l0 4 T. If the induced potential between wingtips is V, what is the plane s speed? a. 250 m/s c. 375 m/s b. 338 m/s d. 417 m/s 16. A bar magnet is falling through a loop of wire with constant velocity. The north pole enters first. As the south pole leaves the loop of wire, the induced current (as viewed from above) will be: a. clockwise. c. zero. b. counterclockwise. d. along the length of the magnet. 17. The wiring in a motor has resistance of 3.0 and produces a back emf of 1.0 V when connected to a 9.0-V battery of negligible resistance. Find the current flow through the motor. a A c. 1.5 A b A d. 2.7 A 18. A motor with a coil resistance of 10 is attached to a voltage supply of 90 V. What is the current in the motor when it is running at its maximum speed with a back emf of 60 V? a. zero c. 6.0 A b. 3.0 A d. 15 A 2

3 19. What is the minimum frequency with which a 200-turn, flat coil of cross sectional area 300 cm 2 can be rotated in a uniform 30-mT magnetic field if the maximum value of the induced emf is to equal 8.0 V? a Hz c. 7.1 Hz b. 2.9 Hz d. 8.4 Hz 20. A coil is rotated in a magnetic field generating an emf given by emf = NBA sin, where = t. At which angle is the emf half of its maximum value? a. 0 c. 45 b. 30 d A motor has an internal resistance of 12. When running, the motor has a back emf of 30 V and draws a current of 4.0 A. What is the supply voltage in this case? a. 30 V c. 78 V b. 48 V d. 120 V 22. The current in a coil with a self-inductance of 1.5 mh increases from 0 to 1.0 A in a tenth of a second. What is the induced emf in the coil? a. 15 mv c V b. 30 mv d V 23. In a circuit made up of inductor L, resistance R, ammeter, battery and switch in series, the current is greatest at which of the following times, as measured after the switch is closed? a. zero c. at a time t = L/R b. one time constant d. ten time constants 24. A coil with a self-inductance of 0.75 mh experiences a constant current buildup from zero to 10 A in 0.25 s. What is the induced emf during this interval? a V c V b V d V 25. What is the self-inductance in a coil that experiences a 3.0-V induced emf when the current is changing at a rate of 110 A/s? a. 83 mh c. 37 mh b. 45 mh d. 27 mh 26. By what factor is the self-inductance of an air solenoid changed if only its number of coil turns, N, is tripled? a. 1/3 c. 6 b. 3 d By what factor is the self-inductance of an air solenoid changed if its length and number of coil turns are both tripled? a. 1/3 c. 6 b. 3 d Two loops of wire are arranged so that a changing current in one, the primary, will induce a current in the other, the secondary. The secondary loop has twice as many turns as the primary loop. As long as the current in the primary is steady at 3 A, the current in the secondary will be: a. 3 A. c. 1.5 A. b. 6 A. d. zero. 3

4 29. Two loops of wire are arranged so that a changing current in one, the primary, will induce a current in the other, the secondary. The secondary loop has twice as many turns as the primary loop. The current in the primary at this moment is 3 A and increasing. The current in the secondary must be: a. 3 A. c. zero. b. 6 A. d. There is insufficient information to work this problem. 30. An air-core inductor has turns/m and an internal volume of 3.0 cm 3. What is its inductance? a. 3.8 H c H b. 38 mh d. Insufficient information is given. 31. An RL series circuit has the following components: 5.0-mH coil, 1.0- resistor, 12-V battery, ammeter and switch. What is the time constant of this circuit? a s c s b s d. 200 s 32. An RL series circuit has: 5.0-mH coil, 1.0- resistor, 12-V battery, ammeter and switch. After the switch is closed for a long time, find the final value of the current. a. 2.5 A c A b. 12 A d A 33. A 12-V battery is connected in series with a switch, resistor and coil. If the circuit s time constant is s and the final steady current after the switch is closed becomes 1.0 A, what is the value of the inductance? a. 1.2 mh c. 9.6 mh b. 2.4 mh d. 48 mh 34. A series circuit contains a 12-V battery, a 2.0- resistor, and a 3.0-mH inductor. If the switch to the battery is closed at t = 0, find the time required for the current in the circuit to reach 63% of its final value. a. 1.5 ms c. 4.0 ms b. 3.0 ms d. 5.0 ms 35. A circuit consists of a 10-mH coil, a 12- resistor, a 6.0- resistor, a 9.0-V battery and a switch, all in series. What is the time constant of this circuit? a s c s b s d s 36. An emf of 0.32 V is induced in a 0.40-H inductor. What is the rate of change of current through the inductor? a A/s c. 1.3 A/s b A/s d A/s 37. What is the stored energy in a 0.50-mH coil carrying a current of 4.0 A? a J c J b J d J 38. A 12-V battery is connected in series with a switch, 6.0- resistor and coil. What energy is stored in the coil when the current is 2.0 A? The time constant is s. a J c J b J d J 4

5 39. Superconductors have been discussed as a means for electrical energy storage. Because they are resistanceless, a current once started in a loop would continue without loss. If a current of A were started in a huge toroidal coil of radius 1.0 km and inductance 50 H, how much electrical energy (in kwh) could be stored? a. 300 kwh c. 690 kwh b. 480 kwh d. 840 kwh 40. An RL circuit has L = 0.40 H and R = 5.0. It is connected to a battery with = 22 V at time t = 0. Find the energy stored in the inductor when the current in the circuit is 0.50 A. a. 50 mj c. 2.0 J b. 1.0 J d. 5.0 J 5

6 ID: A Induction Answer Section MULTIPLE CHOICE 1. B 2. D 3. D 4. D 5. D 6. A 7. C 8. A 9. C 10. A 11. C 12. C 13. D 14. D 15. C 16. A 17. D 18. B 19. C 20. B 21. C 22. A 23. D 24. B 25. D 26. D 27. B 28. D 29. D 30. A 31. B 32. B 33. B 34. A 35. D 36. A 37. B 38. A 39. C 40. A 1

Induced voltages and Inductance Faraday s Law

Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic