Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 31, Problem 42AP
You are working on an LC circuit for an experiment you are performing in your basement. You have an appropriate capacitor, but you need to build your own inductor. You wish to cut a wooden ring with a rectangular cross section, as shown in Figure P31.41, from wood with thickness h. You want to wrap N turns of wire around it to form a toroidal inductor. For your experiment, you need to have energy UB stored in the inductor when it carries a current i. In order to cut the appropriate wooden ring, you need to determine the ratio b/a. Ignore any effect of the wood core on the magnetic field.
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You are working on an LC circuit for an experiment you are performing in your basement. You have an appropriate capacitor, but you need to build your own inductor. You wish to cut a wooden ring with a rectangular cross section, as shown, from wood with thickness h = 1.00 cm. You want to wrap 500 turns of wire around it to form a toroidal inductor. For your experiment, you need to have 1.82 × 10–4 J of energy stored in the inductor when it carries a current of 2.00 A. In order to cut the appropriate wooden ring, you need to determine the ratio b/a. Ignore any effect of the wood core on the magnetic field.
At t = 0, the open switch in Figure P31.46 is thrown closed.
We wish to find a symbolic expression for the current in
the inductor for time t> 0. Let this current be called i and
choose it to be downward in the inductor in Figure P31.46.
Identify i, as the current to the right through R, and iz
as the current downward through R. (a) Use Kirchhoff's
junction rule to find a relation among the three currents.
(b) Use Kirchhoff's loop rule around the left loop to find
another relationship. (c) Use Kirchhoff's loop rule around
the outer loop to find a third relationship. (d) Eliminate
i, and i, among the three equations to find an equation
involving only the current i. (e) Compare the equation in
part (d) with Equation 31.6 in the text. Use this comparison
R
Figure P31.46
to rewrite Equation 31.7 in the text for the situation in this
problem and show that
i(t)
R,
where R' = R,R,/(R, + R,).
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Chapter 31 Solutions
Physics for Scientists and Engineers
Ch. 31.1 - A coil with zero resistance has its ends labeled a...Ch. 31.2 - Prob. 31.2QQCh. 31.3 - Prob. 31.3QQCh. 31.4 - Prob. 31.4QQCh. 31.5 - (i) At an instant of time during the oscillations...Ch. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 31 - Prob. 4PCh. 31 - Prob. 5P
Ch. 31 - A toroid has a major radius R and a minor radius r...Ch. 31 - Prob. 7PCh. 31 - Prob. 8PCh. 31 - Prob. 9PCh. 31 - Prob. 10PCh. 31 - Prob. 11PCh. 31 - Show that i = Iiet/ is a solution of the...Ch. 31 - Prob. 13PCh. 31 - You are working as a demonstration assistant for a...Ch. 31 - Prob. 15PCh. 31 - The switch in Figure P31.15 is open for t 0 and...Ch. 31 - Prob. 17PCh. 31 - Two ideal inductors, L1 and L2, have zero internal...Ch. 31 - Prob. 19PCh. 31 - Prob. 20PCh. 31 - Prob. 21PCh. 31 - Complete the calculation in Example 31.3 by...Ch. 31 - Prob. 23PCh. 31 - A flat coil of wire has an inductance of 40.0 mH...Ch. 31 - Prob. 25PCh. 31 - Prob. 26PCh. 31 - Prob. 27PCh. 31 - Prob. 28PCh. 31 - In the circuit of Figure P31.29, the battery emf...Ch. 31 - Prob. 30PCh. 31 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 31 - Prob. 32PCh. 31 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 31 - Prob. 34PCh. 31 - Electrical oscillations are initiated in a series...Ch. 31 - Review. Consider a capacitor with vacuum between...Ch. 31 - A capacitor in a series LC circuit has an initial...Ch. 31 - Prob. 38APCh. 31 - Prob. 39APCh. 31 - At the moment t = 0, a 24.0-V battery is connected...Ch. 31 - Prob. 41APCh. 31 - You are working on an LC circuit for an experiment...Ch. 31 - Prob. 43APCh. 31 - Prob. 44APCh. 31 - Prob. 45APCh. 31 - At t = 0, the open switch in Figure P31.46 is...Ch. 31 - Review. The use of superconductors has been...Ch. 31 - Review. A fundamental property of a type 1...Ch. 31 - Prob. 49APCh. 31 - In earlier times when many households received...Ch. 31 - Assume the magnitude of the magnetic field outside...Ch. 31 - Prob. 52CPCh. 31 - Prob. 53CP
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