교과서 질문
At t = 0 s, the current in the circuit in FIGURE EX30.35 is I0. At what time in μs is the current (1/2)I0?
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Ch 30: Electromagnetic Induction
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
30장, 문제 29
A 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF. What is the range of oscillation frequencies for this circuit?
검증된 단계별 안내1
Identify the formula for the resonant frequency of an LC circuit: \( f = \frac{1}{2\pi\sqrt{L C}} \), where \( f \) is the frequency, \( L \) is the inductance, and \( C \) is the capacitance.
Convert the given values into standard SI units: \( L = 2.0 \ \text{mH} = 2.0 \times 10^{-3} \ \text{H} \), \( C_{min} = 100 \ \text{pF} = 100 \times 10^{-12} \ \text{F} \), and \( C_{max} = 200 \ \text{pF} = 200 \times 10^{-12} \ \text{F} \).
Calculate the minimum frequency using \( C_{max} \): Substitute \( L = 2.0 \times 10^{-3} \ \text{H} \) and \( C = 200 \times 10^{-12} \ \text{F} \) into the formula \( f = \frac{1}{2\pi\sqrt{L C}} \).
Calculate the maximum frequency using \( C_{min} \): Substitute \( L = 2.0 \times 10^{-3} \ \text{H} \) and \( C = 100 \times 10^{-12} \ \text{F} \) into the formula \( f = \frac{1}{2\pi\sqrt{L C}} \).
The range of oscillation frequencies is from the minimum frequency (calculated with \( C_{max} \)) to the maximum frequency (calculated with \( C_{min} \)).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Inductance
Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. The unit of inductance is the henry (H). In this question, the inductor has a value of 2.0 mH, which will influence the oscillation frequency of the LC circuit.
추천 영상:
가이드 코스
12:59
Mutual Induction
Capacitance
Capacitance is the ability of a component, usually a capacitor, to store electrical energy in an electric field. It is measured in farads (F). The variable capacitor in this circuit can change its capacitance from 100 pF to 200 pF, affecting the resonant frequency of the circuit when combined with the inductor.
추천 영상:
가이드 코스
08:02Capacitors & Capacitance (Intro)
Resonant Frequency
The resonant frequency of an LC circuit is the frequency at which the inductive and capacitive reactances are equal in magnitude, resulting in maximum oscillation. It can be calculated using the formula f = 1/(2π√(LC)), where L is inductance and C is capacitance. This concept is crucial for determining the range of oscillation frequencies for the given inductor and variable capacitor.
추천 영상:
가이드 코스
05:23Resonance in Series LRC Circuits
관련 실천
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The switch in FIGURE EX30.32 has been in position 1 for a long time. It is changed to position 2 at t = 0 s. What is the first time at which the current is maximum?
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