Textbook Question
An L-R-C series circuit has L = 0.450 H, C = 2.50 × 10-5 F, and resistance R. What is the angular frequency of the circuit when R = 0?
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Ch 30: Inductance
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 30, Problem 18b
It has been proposed to use large inductors as energy storage devices. If the amount of energy calculated in part is stored in an inductor in which the current is 80.0 A, what is the inductance?
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Start by recalling the formula for the energy stored in an inductor: \( E = \frac{1}{2} L I^2 \), where \( E \) is the energy, \( L \) is the inductance, and \( I \) is the current.
Rearrange the formula to solve for inductance \( L \): \( L = \frac{2E}{I^2} \).
Identify the values given in the problem: the current \( I = 80.0 \) A and the energy \( E \) which was calculated in part (a).
Substitute the known values into the rearranged formula: \( L = \frac{2E}{(80.0)^2} \).
Ensure units are consistent and calculate \( L \) using the substituted values to find the inductance.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Energy Stored in an Inductor
The energy stored in an inductor is given by the formula E = (1/2)LI^2, where E is the energy, L is the inductance, and I is the current. This relationship shows how energy is related to the inductance and the square of the current flowing through the inductor.
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Energy Stored by Capacitor
Inductance
Inductance is a property of an electrical conductor that quantifies its ability to store energy in a magnetic field when current flows through it. It is measured in henries (H) and depends on factors like the coil's geometry and the core material. Inductance determines how much energy can be stored for a given current.
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Current
Current, measured in amperes (A), is the flow of electric charge through a conductor. In the context of inductors, the current is crucial because the energy stored is proportional to the square of the current. A higher current results in more energy stored, assuming the inductance remains constant.
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Related Practice
Textbook Question
An L-R-C series circuit has L = 0.450 H, C = 2.50 × 10-5 F, and resistance R. What value must R have to give a 5.0% decrease in angular frequency compared to the value calculated in part (a)?
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Textbook Question
It has been proposed to use large inductors as energy storage devices. How much electrical energy is converted to light and thermal energy by a 150 W light bulb in one day?
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Textbook Question
An air-filled toroidal solenoid has a mean radius of 15.0 cm and a cross-sectional area of 5.00 cm2. When the current is 12.0 A, the energy stored is 0.390 J. How many turns does the winding have?
Textbook Question
A solenoid 25.0 cm long and with a cross-sectional area of 0.500 cm2 contains 400 turns of wire and carries a current of 80.0 A. Calculate: the total energy contained in the coil's magnetic field (assume the field is uniform);
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