UNIVERSITY PHYSICS UCI PKG
11th Edition
ISBN: 9781323575208
Author: YOUNG
Publisher: PEARSON C
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Question
Chapter 30, Problem 30.60P
(a)
To determine
The maximum charge that the capacitor receives.
(b)
To determine
The current in the inductor at this time.
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30. A short wire runs along an x axis from x = a to x = -a
(Figure P30.30). At t = 0, there is a small sphere carry-
ing charge +9o at x = a and a small sphere carrying charge
-9o at x = -a. As the spheres discharge and a current is
established in the wire, show that, for t>0, the generalized
form of Ampère's law (Eq. 30.13) and the Biot-Savart law
(Eq. 28.12) give the same result for the magnitude of the mag-
netic field a distance b up the y axis. (Hint: Obtain the elec-
tric flux through a circular disk in the yz plane, centered at
the origin. Because the electric field is not constant over the
surface of the disk, you must divide the disk into a nested set
of rings of various radii and integrate. A representative ring
should have radius r and radial extent dr.) •..
Figure P30.30
b
-90
A resistor and inductor are connected to a 9.0 V battery by a switch as shown. The moment the switch is closed, current flows through the circuit. The resistor has a resistance of R = 440 Ω and the inductor has an inductance of L = 150 mH.
a) write an equation that relates the current as a function of time i(t) to the maximum current, imax. Express the equation in terms of imax and α, where α = -t/T (time constant).
b) determine the time, in seconds, at which the current has a value of i(t50) = 50% of imax.
c) determine the time, in seconds, at which the current has a value of i(t99) = 99% of imax.
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Chapter 30 Solutions
UNIVERSITY PHYSICS UCI PKG
Ch. 30.1 - Consider the Tesla coil described in Example 30.1....Ch. 30.2 - Prob. 30.2TYUCh. 30.3 - Prob. 30.3TYUCh. 30.4 - Prob. 30.4TYUCh. 30.5 - Prob. 30.5TYUCh. 30.6 - An L-R-C series circuit includes a 2.0- resistor....Ch. 30 - In an electric trolley or bus system, the vehicles...Ch. 30 - From Eq. (30.5) 1 H = 1 Wb/A. and from Eqs. (30.4)...Ch. 30 - Prob. 30.3DQCh. 30 - Prob. 30.4DQ
Ch. 30 - Prob. 30.5DQCh. 30 - Two closely wound circular coils have the same...Ch. 30 - Prob. 30.7DQCh. 30 - For the same magnetic field strength B, is the...Ch. 30 - Prob. 30.9DQCh. 30 - A Differentiating Circuit. The current in a...Ch. 30 - In Section 30.5 Kirchhoffs loop rule is applied to...Ch. 30 - Prob. 30.12DQCh. 30 - Prob. 30.13DQCh. 30 - In the R-L circuit shown in Fig. 30.11, is the...Ch. 30 - Prob. 30.15DQCh. 30 - In an L-R-C series circuit, what criteria could be...Ch. 30 - Prob. 30.1ECh. 30 - Prob. 30.2ECh. 30 - Prob. 30.3ECh. 30 - Prob. 30.4ECh. 30 - Prob. 30.5ECh. 30 - Prob. 30.6ECh. 30 - A 2.50-mH toroidal solenoid has an average radius...Ch. 30 - Prob. 30.8ECh. 30 - Prob. 30.9ECh. 30 - Prob. 30.10ECh. 30 - Prob. 30.11ECh. 30 - Prob. 30.12ECh. 30 - Prob. 30.13ECh. 30 - A long, straight solenoid has 800 turns. When the...Ch. 30 - Prob. 30.15ECh. 30 - Prob. 30.16ECh. 30 - Prob. 30.17ECh. 30 - Prob. 30.18ECh. 30 - Prob. 30.19ECh. 30 - Prob. 30.20ECh. 30 - In a proton accelerator used in elementary...Ch. 30 - It is proposed to store l.00 kWh = 3.60 106J of...Ch. 30 - Prob. 30.23ECh. 30 - Prob. 30.24ECh. 30 - Prob. 30.25ECh. 30 - In Fig. 30.11, switch S1 is closcd while switch S2...Ch. 30 - In Fig. 30.11, suppose that = 60.0 V, R = 240 ,...Ch. 30 - Prob. 30.28ECh. 30 - Prob. 30.29ECh. 30 - Prob. 30.30ECh. 30 - In an L-C circuit. L = 85.0 mH and C = 3.20F....Ch. 30 - Prob. 30.32ECh. 30 - A 7.50-nF capacitor is charged up to 12.0 V, then...Ch. 30 - Prob. 30.34ECh. 30 - Prob. 30.35ECh. 30 - A Radio Tuning Circuit. The minimum capacitance of...Ch. 30 - An L-C circuit containing an 80.0-mH inductor and...Ch. 30 - An L-R-C series circuit has L = 0.600 H and C =...Ch. 30 - Prob. 30.39ECh. 30 - An L-R-C series circuit has L = 0.400 H, C = 7.00...Ch. 30 - Prob. 30.41ECh. 30 - Prob. 30.42PCh. 30 - Prob. 30.43PCh. 30 - Prob. 30.44PCh. 30 - Solar Magnetic Energy. Magnetic fields within a...Ch. 30 - CP CALC A Coaxial Cable. A small solid conductor...Ch. 30 - Prob. 30.47PCh. 30 - CALC Consider the circuit in Fig. 30.11 with both...Ch. 30 - Prob. 30.49PCh. 30 - Prob. 30.50PCh. 30 - Prob. 30.51PCh. 30 - Prob. 30.52PCh. 30 - Prob. 30.53PCh. 30 - A 6.40-nF capacitor is charged to 24.0 V and then...Ch. 30 - An L-C circuit consists of a 60.0-mH inductor and...Ch. 30 - A charged capacitor with C = 590 F is connected in...Ch. 30 - CP In the circuit shown in Fig. P30.57, the switch...Ch. 30 - Prob. 30.58PCh. 30 - Prob. 30.59PCh. 30 - Prob. 30.60PCh. 30 - Prob. 30.61PCh. 30 - Prob. 30.62PCh. 30 - Prob. 30.63PCh. 30 - After the current in the circuit of Fig. P30.63...Ch. 30 - CP In the circuit shown in Fig. P30.65, switch S...Ch. 30 - Prob. 30.66PCh. 30 - Prob. 30.67PCh. 30 - Prob. 30.68PCh. 30 - Prob. 30.69PCh. 30 - CP A Volume Gauge. A tank containing a liquid has...Ch. 30 - Prob. 30.71CPCh. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...Ch. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...Ch. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...Ch. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...
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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_forwardEach of the three situations in Figure P32.68 shows a resistor in a circuit in which currents are induced. Using Lenzs law, determine whether the current in each situation is from a to b or from b to a. a. If the current I in the wire in Figure P32.68A is increased from zero to I, what is the direction of the current induced across the resistor R? b. The switch in Figure P32.68B is initially closed and is thrown open at t = 0. What is the direction of the current induced across the resistor R immediately afterward? c. A bar magnet is brought close to the circuit shown in Figure P32.68C. What is the direction of the current induced across the resistor R?arrow_forwardA coil with a self-inductance of 3.0 H and a resistance of 100 2 carries a steady current of 2.0 A. (a) What is the energy stored in the magnetic field of the coil? (b) What is the energy per second dissipated in the resistance of the coil?arrow_forward
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- Figure P23.58 is a graph of the induced emf versus time for a coil of N turns rotating with angular speed ω in a uniform magnetic field directed perpendicular to the coil’s axis of rotation. What If? Copy this sketch (on a larger scale) and on the same set of axes show the graph of emf versus t (a) if the number of turns in the coil is doubled, (b) if instead the angular speed is doubled, and (c) if the angular speed is doubled while the number of turns in the coil is halved. Figure P23.58arrow_forwardA conducting rod of length moves with velocity v parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with the near end a distance r away (Fig. P30.44). Show that the magnitude of the emf induced in the rod is E=0Iv2ln(1+lr) Figure P30.44arrow_forwardA thin wire = 30.0 cm long is held parallel to and d = 80.0 cm above a long, thin wire carrying I = 200 A and fixed in position (Fig. P30.47). The 30.0-cm wire is released at the instant t = 0 and falls, remaining parallel to the current-carrying wire as it falls. Assume the falling wire accelerates at 9.80 m/s2. (a) Derive an equation for the emf induced in it as a function of time. (b) What is the minimum value of the emf? (c) What is the maximum value? (d) What is the induced emf 0.300 s after the wire is released? Figure P30.47arrow_forward
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