Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 32, Problem 42PQ
Suppose you have a simple homemade AC generator like the one in Figure 32.20 (page 1026) whose emf is about half of what you need to power a particular motor. How can you easily modify the generator to suit your needs? Explain your modifications specifically.
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A 15.00 µF capacitor, labeled as C below, is charged to 175.0 µC at time t = 0. At t = 0, the capacitor is connected across the ends of a 5.00 mH inductor represented by symbol L. The diagram below shows the system just after the fully charged capacitor C is connected to inductor L. The current I just begins to flow at t = 0, reducing the charge Q on the right plate.
(a) What is the angular frequency ω of the charge oscillations in the capacitor after the above connection is made?
(b) Find the maximum current IMAX.
(c) What is the value of charge Q on the right plate when the current I reaches the maximum value IMAX?
In an oscillating LC circuit in which C = 4.00 mF, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 mA.What are (a) the inductance L and (b) the frequency of the oscillations? (c) How much time is required for the charge on the capacitor to rise from zero to its maximum value?
When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin ωt represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is εmax = μ0nAωImax. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose.
Chapter 32 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 32.1 - To calculate the magnetic flux through the...Ch. 32.2 - Prob. 32.2CECh. 32.3 - Prob. 32.3CECh. 32.3 - Prob. 32.4CECh. 32.4 - Prob. 32.5CECh. 32.5 - Prob. 32.6CECh. 32.6 - Prob. 32.7CECh. 32.8 - Prob. 32.8CECh. 32.8 - Prob. 32.9CECh. 32 - A constant magnetic field of 0.275 T points...
Ch. 32 - Prob. 2PQCh. 32 - Prob. 3PQCh. 32 - Prob. 4PQCh. 32 - Prob. 5PQCh. 32 - Figure P32.6 shows three situations involving a...Ch. 32 - A rectangular loop of length L and width W is...Ch. 32 - The magnetic field through a square loop of wire...Ch. 32 - Prob. 9PQCh. 32 - Prob. 10PQCh. 32 - Suppose a uniform magnetic field is perpendicular...Ch. 32 - Prob. 12PQCh. 32 - A square conducting loop with side length a = 1.25...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - Prob. 16PQCh. 32 - Prob. 17PQCh. 32 - Prob. 18PQCh. 32 - A square loop with side length 5.00 cm is on a...Ch. 32 - A thin copper rod of length L rotates with...Ch. 32 - Figure P32.21 shows a circular conducting loop...Ch. 32 - Prob. 22PQCh. 32 - A square loop with side length L, mass M, and...Ch. 32 - Prob. 24PQCh. 32 - Prob. 25PQCh. 32 - Prob. 26PQCh. 32 - Prob. 27PQCh. 32 - A solenoid of area Asol produces a uniform...Ch. 32 - Two circular conductors are perpendicular to each...Ch. 32 - Two circular conducting loops labeled A and B are...Ch. 32 - Prob. 31PQCh. 32 - Prob. 32PQCh. 32 - Prob. 33PQCh. 32 - Prob. 34PQCh. 32 - Prob. 35PQCh. 32 - Find an expression for the current in the slide...Ch. 32 - The slide generator in Figure 32.14 (page 1020) is...Ch. 32 - Prob. 38PQCh. 32 - A thin conducting bar (60.0 cm long) aligned in...Ch. 32 - A stiff spring with a spring constant of 1200.0...Ch. 32 - A generator spinning at a rate of 1.20 103...Ch. 32 - Suppose you have a simple homemade AC generator...Ch. 32 - Prob. 43PQCh. 32 - Prob. 44PQCh. 32 - Prob. 45PQCh. 32 - Prob. 46PQCh. 32 - A square coil with a side length of 12.0 cm and 34...Ch. 32 - Prob. 48PQCh. 32 - Prob. 49PQCh. 32 - Prob. 50PQCh. 32 - Prob. 51PQCh. 32 - Prob. 52PQCh. 32 - Prob. 53PQCh. 32 - Prob. 54PQCh. 32 - Prob. 55PQCh. 32 - Prob. 56PQCh. 32 - Prob. 57PQCh. 32 - A step-down transformer has 65 turns in its...Ch. 32 - Prob. 59PQCh. 32 - Prob. 60PQCh. 32 - Prob. 61PQCh. 32 - Prob. 62PQCh. 32 - Prob. 63PQCh. 32 - A bar magnet is dropped through a loop of wire as...Ch. 32 - Prob. 65PQCh. 32 - Prob. 66PQCh. 32 - A circular coil with 75 turns and radius 12.0 cm...Ch. 32 - Each of the three situations in Figure P32.68...Ch. 32 - A square loop with sides 1.0 m in length is placed...Ch. 32 - Prob. 70PQCh. 32 - Two frictionless conducting rails separated by l =...Ch. 32 - Imagine a glorious day after youve finished...Ch. 32 - Prob. 73PQCh. 32 - A Figure P32.74 shows an N-turn rectangular coil...Ch. 32 - A rectangular conducting loop with dimensions w =...Ch. 32 - Prob. 76PQCh. 32 - A conducting rod is pulled with constant speed v...Ch. 32 - Prob. 78PQCh. 32 - A conducting single-turn circular loop with a...Ch. 32 - A metal rod of mass M and length L is pivoted...
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- When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P23.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin t represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is Emax=0nAImax. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P23.8arrow_forwardIn an oscillating LC circuit in which C = 4.5 μF, the maximum potential difference across the capacitor during the oscillations is 1.5 V and the maximum current through the inductor is 52.8 mA. What are (a) the inductance L and (b) the frequency of the oscillations? (c) How much time is required for the charge on the capacitor to rise from zero to its maximum value?arrow_forwardYou are to design an AC generator that has 800 circular windings, each with a radius of 1.75m. The generator is to produce a peak voltage of 12000V that oscillates with a frequency of 60Hz. What magnetic field should be used to accomplish this?arrow_forward
- In a model AC generator, a 495 turn rectangular coil 10.0 cm by 23 cm rotates at 123 rev/min in a uniform magnetic field of 0.55 T. (a) What is the maximum emf induced in the coil? (b) What is the instantaneous value of the emf in the coil at t = (?/33) s? Assume that the emf is zero at t = 0. (c) What is the smallest value of t for which the emf will have its maximum value?arrow_forwardA series RLC circuit driven by a source with an amplitude of 120.0 V and a frequency of 50.0 Hz has an inductance of 787 mH, a resistance of 267 , and a capacitance of 45.7 F. a. What are the maximum current and the phase angle between the current and the source emf in this circuit? b. What are the maximum potential difference across the inductor and the phase angle between this potential difference and the current in the circuit? c. What are the maximum potential difference across the resistor and the phase angle between this potential difference and the current in this circuit? d. What are the maximum potential difference across the capacitor and the phase angle between this potential difference and the current in this circuit?arrow_forwardIn the LC circuit in Figure 33.11, the inductance is L = 19.8 mH and the capacitance is C = 19.6 mF. At some moment, UB = UE= 17.5 mJ. a. What is the maximum charge stored by the capacitor? b. What is the maximum current in the circuit? c. At t = 0, the capacitor is fully charged. Write an expression for the charge stored by the capacitor as a function of lime. d. Write an expression for the current as a function of time.arrow_forward
- A resistor and inductor are connected in series across an ac generator. The emf of the generator is given by v(t)=V0cost , where V0=120V and =120rad/s ; also, R=400 and L = 1.5 H. (a) What Is the impedance of the circuit? (b) What is the amplitude of the current through the resistor? (C) Write an expression for the current through the resistor. (d) Write expressions representing the voltages across the resistor and across the inductor.arrow_forwardA 7.0-mH induct is connected across a 60-Hz ac source whose voltage amplitude is 50 V. (a) What is the maximum current through the inductor? (b) What is the phase relationship between the current through and the potential difference across the inductor?arrow_forwardThe emf of an ac source is given by v(t)=V0sint, where V0=100V and =200 . Find an expression that represents the output current of the source if it is connected across (a) a 20-pF capacitor, (b) a 20-mH inductor, and (c) a 50 resistor.arrow_forward
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