Textbook Question
An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. Calculate the angular frequency of oscillation for the circuit when R = 0.
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Ch 30: Inductance
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 30, Problem 39a
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?
Verified step by step guidance1
Start by understanding the concept of an L-R-C series circuit, which consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. The angular frequency of such a circuit is determined by the inductance and capacitance when the resistance is zero.
Recall the formula for the angular frequency \( \omega \) of an L-R-C circuit when the resistance \( R = 0 \). The formula is given by \( \omega = \frac{1}{\sqrt{LC}} \). This formula is derived from the resonance condition of the circuit.
Substitute the given values into the formula. Here, \( L = 0.450 \) H and \( C = 2.50 \times 10^{-5} \) F. The substitution will look like \( \omega = \frac{1}{\sqrt{0.450 \times 2.50 \times 10^{-5}}} \).
Simplify the expression inside the square root. Calculate \( 0.450 \times 2.50 \times 10^{-5} \) to find the product of the inductance and capacitance.
Finally, take the square root of the product calculated in the previous step and then find the reciprocal to determine the angular frequency \( \omega \). This will give you the angular frequency of the circuit when \( R = 0 \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Frequency in L-R-C Circuits
Angular frequency in an L-R-C circuit is a measure of how rapidly the circuit oscillates. When resistance R is zero, the circuit is purely oscillatory, and the angular frequency is determined by the inductance (L) and capacitance (C) using the formula ω = 1/√(LC). This frequency is crucial for understanding the natural oscillations of the circuit.
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LRC Circuits
Inductance
Inductance (L) is a property of a coil or inductor that quantifies its ability to store energy in a magnetic field when electrical current flows through it. In an L-R-C circuit, inductance affects the rate of change of current and plays a key role in determining the circuit's angular frequency, especially when resistance is negligible.
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Capacitance
Capacitance (C) is the ability of a capacitor to store electrical energy in an electric field. It is a measure of how much charge a capacitor can hold per unit voltage. In an L-R-C circuit, capacitance influences the oscillation frequency, as it determines how quickly the circuit can charge and discharge, affecting the angular frequency when resistance is zero.
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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
An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. What value of R gives critical damping?
Textbook Question
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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