Domanda del libro di testo
For the circuit of FIGURE EX32.32, What is the resonance frequency, in both rad/s and Hz?
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Ch 32: AC Circuits
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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
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Capitolo 32, Problema 28
A series RLC circuit has a 200 kHz resonance frequency. What is the resonance frequency if the capacitor value is doubled and, at the same time, the inductor value is halved?
Guida verificata passo dopo passo1
Identify the formula for the resonance frequency of an RLC circuit, which is given by \( f = \frac{1}{2\pi\sqrt{LC}} \), where \( L \) is the inductance, \( C \) is the capacitance, and \( f \) is the resonance frequency.
Note the changes in the circuit components: the capacitor value is doubled (\( C' = 2C \)) and the inductor value is halved (\( L' = \frac{L}{2} \)).
Substitute the new values of \( L' \) and \( C' \) into the resonance frequency formula to find the new resonance frequency \( f' \). Use \( f' = \frac{1}{2\pi\sqrt{L' \cdot C'}} \).
Simplify the expression by substituting \( L' = \frac{L}{2} \) and \( C' = 2C \) into the formula, resulting in \( f' = \frac{1}{2\pi\sqrt{\frac{L}{2} \cdot 2C}} \).
Further simplify the expression to find that the new resonance frequency \( f' \) is equal to the original resonance frequency \( f \), because the changes in \( L \) and \( C \) counteract each other.
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Resonance Frequency in RLC Circuits
The resonance frequency of a series RLC circuit is the frequency at which the inductive reactance equals the capacitive reactance, resulting in maximum current flow. It is given by the formula f₀ = 1 / (2π√(LC)), where L is the inductance and C is the capacitance. At resonance, the impedance of the circuit is minimized, and the circuit can oscillate freely.
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05:23
Resonance in Series LRC Circuits
Effect of Capacitance on Resonance Frequency
Doubling the capacitance in an RLC circuit affects the resonance frequency inversely. According to the resonance frequency formula, increasing capacitance decreases the resonance frequency, as it is in the denominator of the square root. This means that if the capacitance is doubled, the resonance frequency will decrease, leading to a lower frequency of oscillation.
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05:23Resonance in Series LRC Circuits
Effect of Inductance on Resonance Frequency
Halving the inductance in an RLC circuit also influences the resonance frequency, but in the opposite direction. Since inductance is also in the denominator of the square root in the resonance frequency formula, reducing the inductance increases the resonance frequency. Therefore, if the inductance is halved, the resonance frequency will increase, resulting in a higher frequency of oscillation.
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05:23Resonance in Series LRC Circuits
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A series RLC circuit has a 200 kHz resonance frequency. What is the resonance frequency if the capacitor value is doubled?
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