Physics 240 Fall 2005: Exam #3 Please print your name: Please list your discussion section number: Please list your discussion instructor: Form #1 Instructions 1. Fill in your name above 2. This will be a 1.5 hour, closed book exam. The exam includes 20 questions. 3. You may use a calculator, please do not share calculators 4. You may use three 3 x5 note cards (two from the earlier exams, plus one new one) with notes and equations you think may be useful. You can write on both sides of the card if you like. 5. You will be asked to show your University student ID card when you turn in your exam. ID checked by: Table of constants: ε 0 = 8.85 x 10-12 C 2 /Nm 2 k = 1/(4πε 0 ) q electron =-1.6 x 10-19 C q proton =1.6 x 10-19 C m electron =9.1 x 10-31 kg m proton =1.67 x 10-27 kg μ 0 = 4π x 10-7 Tm/A G = 6.67 x 10-11 Nm 2 /kg 2
1: A zero resistance rod slides to the right on zero resistance rails separated by 0.3 m. The rails are connected by a 25 Ω resistor. A constant magnetic field of 0.05 T permeates the region, coming straight out of the page. Find the speed at which the bar must be moved to produce a current of 0.01A in the resistor. a) 34 m/s b) 17 m/s c) 89 m/s d) 50 m/s e) 28 m/s R = 25 Ω v 0.3 m 2: Four different loops of wire will move to the right with the same velocity from a region of zero field, into a region with constant field B. Rank them from least to greatest according to the maximum magnitude of the induced EMF they will feel. Relative heights and widths are listed below each loop. a) 1 is least, then 2 and 4 tie, and 3 is greatest b) 2 and 3 are tied for least, 1 and 4 are tied for greatest c) 3 is least, 4 is larger, and 1 and 2 are tied for greatest d) 3 is least, 2 and 4 are tied and larger, 1 is greatest e) 2 and 4 are tied for least, 3 is larger, 1 is greatest 1 2 3 4. 2W x 3H 3W x 2H 3W x 1H 2W x 2H
3: A small bar magnet is dropped from the same position below the centers of several different loops of wire, each of which is held fixed in place. Loop A has resistance 2R, loop B has resistance R, and loop C has a small break in it. Which of the following statements is correct? a) The magnet accelerates downward at the same rate in each case b) The magnet accelerates down away from loop C, but accelerates up towards loops A and B c) The magnet accelerates down away all loops, most rapidly from B, most slowly away from C d) The magnet accelerates down away slowly from loop A, down more rapidly from loop C, and up towards loop B e) The magnet accelerates down away from all loops, most rapidly from C, most slowly from B A B C N S N S N S 4: Consider the circuit shown, which contains a 60 V battery, a 50 Ω resistor, a light bulb with resistance 50 Ω, and a 100 H inductor. What is the current through the bulb long after the switch is closed? Assume the inductor has zero resistance. a) 1.2 A b) 0.4 A c) 0.6 A d) Zero e) 1.6 A 50 Ω 60 V 50 Ω 100 H
5: Most contemporary high voltage power lines operate at 380,000 V RMS. There are efforts to build new power lines which operate at 760,000 V RMS. If we switch to these new lines, keeping the resistance of the cables themselves the same and still transmitting the same total power, how will this affect power transmission? a) Current in the lines will increase by a factor 2 b) Ohmic energy losses in the wires will decrease by a factor of 2 c) Ohmic energy losses in the wires will increase by a factor of 2 d) Ohmic energy losses in the wires will decrease by a factor of 4 e) Ohmic energy losses in the wires will remain the same 6: The circuit shown is in a uniform magnetic field which points into the page. The magnitude of this field is decreasing at a rate of 150 T/s. What is the current in this loop while this is happening? a) 0.18 A b) 0.22 A c) 0.40 A d) 0.62 A e) 0.34 A 12 cm 12 cm 10 Ω 4 V
7: A resistor, an inductor and an initially charged capacitor are wired together in series. Charge on the capacitor then oscillates and gradually drains away. We could slow down the exponential decay of the maximum charge on the capacitor plates by: a) Decreasing the inductance b) Increasing the resistance c) Decreasing the resistance d) Increasing the capacitance e) Decreasing the capacitance 8: An AC generator producing a maximum voltage of 10 V at an angular frequency of 200 rad/s is connected in series with a 50 Ω resistor, a 400 mh inductor, and a 200 μf capacitor. What is the peak current in this circuit? a) 0.125 A b) 0.135 A c) 0.18 A d) 0.20 A e) 0.40 A
9: In an AC circuit, a 0.025 H inductor is connected to a generator that has an RMS voltage of 25 V and operates at 50 Hz. What is the RMS current through the inductor? a) 0.62 A b) 2.0 A c) 3.2 A d) 7.1 A e) 14 A 10: The electric field within the circular region of radius r shown in the picture points out of the page, and is increasing in magnitude according to the equation: E = C + Dt where C and D are constants. What is the magnitude of the magnetic field at the point P, a distance R (which is greater than r) from the center of the circle? a) C B = μ 0 ε 0 2r b) D B = μ 0 2R c) 2 R B = μ 0 ε 0 D 2r d) 2 r B = μ 0 ε 0 D 2R e) D B = μ 0 ε 0 2R R P r
11: A current sheet is constructed by flowing current uniformly through a thin sheet of metal aligned with the x-axis. The sheet is 2 m wide and 10 m long and carries a total current of 3.0 A. Estimate the magnitude of the magnetic field a distance of 3 cm above the center of the plate. a) 3.3x10-8 T b) 5.1x10-4 T c) 9.4x10-7 T d) 6.9x10-11 T e) 8.9x10-5 T I y x z 10 m 2 m 12: A metal rod with length L and electrical resistance R moves through a constant uniform magnetic field B coming out of the page. What force must be applied to the rod to keep it moving at a constant velocity v? a) 0 b) BLv c) BLv/R d) B 2 L 2 v/r e) B 2 L 2 v 2 /R F? v
13: A single circuit element is connected to an AC generator. It is driven at an angular frequency of 4000 rad/s. The voltage across and current through this circuit are shown in the graph. Which of the following statements about the circuit element is true? a) It must be a capacitor with C = 2.5x10-5 F b) It must be an inductor with L = 2.5x10-3 H c) It must be a resistor with R = 10 Ω d) It must be a capacitor with C = 4x10-7 F e) It must be an inductor with L = 4x10-5 H 14: An 8.0 mh inductor and a 2.0 Ω resistor are wired in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The current reaches half its final value at time: a) 2.8 ms b) 4.0 ms c) 0.52 ms d) 170 μs e) 3 s
15: In an LC circuit in which oscillations of charge and current are occurring, at the moment when the current is zero: a) the charge on the capacitor is zero. b) the energy in the electric field is a maximum. c) the energy in the magnetic field is a maximum. d) the charge is moving through the inductor. e) the energy is shared equally between electric and magnetic field. 16: A circular coil has 275 turns and a radius of 0.045 m. The coil is used as an AC generator by rotating it in a 0.5 T magnetic field. At what angular speed should the coil be rotated to achieve a maximum EMF of 175 V? a) 28 rad/s b) 50 rad/s c) 130 rad/s d) 200 rad/s e) 490 rad/s
17: The figure below shows the total impedance of a series RLC circuit as a function of the driving angular frequency ω. What can you say about the reactance of the resistor R in this circuit? a) Its value depends on frequency ω b) It dominates the impedance at low frequency c) It dominates the impedance at high frequency d) Its value is 500 Ω e) Its value is 100 Ω Impedance Z (in Ω) Angular frequency ω 18: In the same circuit described in the previous problem, at which of the following driving frequencies does the current lead the voltage by the largest amount? a) 1200 rad/s b) 3560 rad/s c) 5000 rad/s d) 7800 rad/s e) 12800 rad/s
19: In class we viewed a demonstration in which a small magnet was slid down two different slabs, each inclined to the same slope. We saw that the magnet accelerated rather freely down the insulating slab, but slid at a slow and constant rate down the nonmagnetic aluminum slab. Which of the following statements is correct? a) The magnet slid freely down the insulating slab because no EMF was induced in the insulating slab b) The magnet more slowly down the metal slab because of the larger surface friction between the magnet and the metal slab c) The magnet slid at a constant rate down the metal slab because it was subject to a velocity dependent force caused by eddy currents in the metal slab d) The magnet slid at a constant rate down the metal slab because it was subject to a velocity independent force caused by eddy currents as it slid down the slab e) The magnet slid rapidly down the insulating slab it was subject to a downward force caused by eddy currents 20: Two closed loops lie near one another on a table. Each loop has a total resistance of 150 Ω. When the current in loop A is increased smoothly from zero to 2.0 A over an interval of 30 ms, a current of 22 ma is induced in loop B. What is the mutual inductance of these two loops? a) 6.2x10-3 H b) 5.0x10-2 H c) 2.9x10-4 H d) 7.1x10-5 H e) 3.1x10-7 H