Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 31, Problem 41AP
To determine
The ratio
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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.
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 below, 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 of i. In order to cut the appropriate wooden ring, you need to determine the ratio
Ignore any effect of the wood core on the magnetic field. (Use any variable or symbol stated above along with the following as necessary: μ0.)
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. 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.
Chapter 31 Solutions
Physics for Scientists and Engineers with Modern Physics
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 - Prob. 3PCh. 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 - Prob. 12PCh. 31 - Prob. 13PCh. 31 - You are working as a demonstration assistant for a...Ch. 31 - Prob. 15PCh. 31 - Prob. 16PCh. 31 - Prob. 17PCh. 31 - Prob. 18PCh. 31 - Prob. 19PCh. 31 - Prob. 20PCh. 31 - Prob. 21PCh. 31 - Prob. 22PCh. 31 - Prob. 23PCh. 31 - Prob. 24PCh. 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 - Prob. 31PCh. 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 - Prob. 36APCh. 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 - Prob. 42APCh. 31 - Prob. 43APCh. 31 - Prob. 44APCh. 31 - Prob. 45APCh. 31 - At t = 0, the open switch in Figure P31.46 is...Ch. 31 - Prob. 47APCh. 31 - Prob. 48APCh. 31 - Prob. 49APCh. 31 - Prob. 50CPCh. 31 - Prob. 51CPCh. 31 - Prob. 52CPCh. 31 - Prob. 53CP
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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_forwardThe magnetic field through a square loop of wire with sides of length 3.00 cm changes with time as shown in Figure P32.8, where the sign indicates the direction of the field relative to the axis of the loop. Plot the emf induced in the loop versus time. FIGURE P32.8arrow_forwardA rectangular loop of length L and width W is placed in a uniform magnetic field B with its plane perpendicular to the field (Fig. P32.7). Determine the time-averaged induced emf if the loop rotatas with constant angular velocity through an angle of 180 around an axis passing through the loops center a. perpendicular to the loop and b. parallel to its width.arrow_forward
- 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,).arrow_forwardIn the circuit of Figure P31.29, the battery emf is 50.0 V, the resistance is 250 V, and the capacitance is 0.500 ?F. The switch S is closed for a long time interval, and zero potential difference is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance?arrow_forwardCan you solve problem #53 in the picture below?arrow_forward
- You are working as an electrical technician. One day, out in the field, you need an inductor but cannot find one. Looking in your wire supply cabinet, you find a cardboard tube with single-conductor wire wrapped uniformly around it to form a solenoid. You carefully count the turns of wire and find that there are 580 turns. The diameter of the tube is 8.00 cm, and the length of the wire-wrapped portion is 36.0 cm. You pull out your calculator to determine (a) the inductance of the coil and (b) the emf generated in it if thecurrent in the wire increases at the rate of 4.00 A/s.arrow_forwardI just need parts A, E, and F. Thank you! A 10.0 μF capacitor is charged to 175 μC and then connected across the ends of a 6.00 mH inductor. (A) Find the maximum current in the inductor. Express your answer with the appropriate units. (E) Find the maximum energy stored in the inductor. Express your answer with the appropriate units. (F) At the instant the energy stored in the inductor is maximum, what is the current in the circuit? Express your answer with the appropriate units.arrow_forwardI need help with a physics problemarrow_forward
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