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 32b
For the circuit of FIGURE EX32.32, Find VR and VL at resonance.
Guida verificata passo dopo passo1
Step 1: Identify the components in the circuit. The circuit consists of a resistor (R = 10 Ω), an inductor (L = 10 mH), and a capacitor (C = 10 μF) connected in series with an AC voltage source of amplitude 10 V and frequency ω.
Step 2: Understand resonance in an RLC circuit. At resonance, the inductive reactance (XL) and capacitive reactance (XC) are equal, causing their effects to cancel each other out. The impedance of the circuit is purely resistive, equal to R.
Step 3: Calculate the resonance angular frequency (ω₀). The resonance condition is given by ω₀ = 1 / √(LC). Substitute L = 10 mH and C = 10 μF into the formula to find ω₀.
Step 4: Determine the voltage across the resistor (VR) at resonance. At resonance, the total voltage of the source is dropped across the resistor. Use Ohm's Law: VR = I × R, where I is the current. The current can be calculated as I = V / R, where V is the source voltage.
Step 5: Determine the voltage across the inductor (VL) at resonance. Even though the inductive reactance cancels the capacitive reactance, the voltage across the inductor can be calculated using VL = I × XL, where XL = ω₀ × L. Substitute the values of I, ω₀, and L to find VL.
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Resonance in RLC Circuits
Resonance occurs in RLC circuits when the inductive reactance (XL) equals the capacitive reactance (XC). At this point, the circuit can oscillate at its natural frequency, maximizing the current flow. The resonance frequency can be calculated using the formula f0 = 1/(2π√(LC)), where L is the inductance and C is the capacitance.
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Percorso guidato
05:23
Resonance in Series LRC Circuits
Voltage Across Components
In an RLC circuit, the voltage across each component (resistor, inductor, and capacitor) can be determined using Ohm's law and the impedance of the circuit. At resonance, the total impedance is minimized, and the voltage across the resistor (VR) can be calculated using the current through the circuit and the resistance value.
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07:14RMS Current and Voltage
Impedance in AC Circuits
Impedance (Z) in AC circuits is the total opposition to current flow, combining resistance (R) and reactance (X). It is expressed as Z = R + j(XL - XC), where j is the imaginary unit. At resonance, the impedance is purely resistive, simplifying calculations for voltages across the components.
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08:40Impedance in AC Circuits
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