Textbook Question
A series RLC circuit consists of a 75 Ω resistor, a 0.12 H inductor, and a 30 μF capacitor. It is attached to a 120 V/60 Hz power line. What is the peak current I?
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Ch 32: AC Circuits
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
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 32, Problem 51b
A series RLC circuit consists of a 75 Ω resistor, a 0.12 H inductor, and a 30 μF capacitor. It is attached to a 120 V/60 Hz power line. What is the phase angle ϕ?
Verified step by step guidance1
Determine the angular frequency (ω) of the AC source using the formula ω = 2πf, where f is the frequency of the power line (60 Hz).
Calculate the inductive reactance (X_L) using the formula X_L = ωL, where L is the inductance of the inductor (0.12 H).
Calculate the capacitive reactance (X_C) using the formula X_C = 1 / (ωC), where C is the capacitance of the capacitor (30 μF or 30 × 10⁻⁶ F).
Find the net reactance (X) of the circuit by subtracting the capacitive reactance from the inductive reactance: X = X_L - X_C.
Calculate the phase angle (ϕ) using the formula tan(ϕ) = X / R, where R is the resistance (75 Ω). Then, take the arctangent of the result to find ϕ in radians or degrees, depending on the desired unit.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Impedance in RLC Circuits
Impedance is the total opposition that a circuit offers to the flow of alternating current (AC) and is represented as a complex number. In a series RLC circuit, the impedance (Z) combines the resistance (R), inductive reactance (XL), and capacitive reactance (XC). The formula for impedance is Z = √(R² + (XL - XC)²), where XL = 2πfL and XC = 1/(2πfC), with f being the frequency.
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08:40
Impedance in AC Circuits
Phase Angle in AC Circuits
The phase angle (ϕ) in an AC circuit indicates the phase difference between the voltage and the current. It is calculated using the formula ϕ = arctan((XL - XC) / R). A positive phase angle indicates that the circuit is inductive, while a negative angle indicates a capacitive circuit. The phase angle is crucial for understanding power factor and energy consumption in AC systems.
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07:14Inductors in AC Circuits
Resonance in RLC Circuits
Resonance occurs in RLC circuits when the inductive reactance equals the capacitive reactance (XL = XC), resulting in maximum current flow and minimal impedance. At resonance, the phase angle is zero, meaning the voltage and current are in phase. Understanding resonance is important for analyzing circuit behavior at different frequencies and optimizing performance in AC applications.
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05:23Resonance in Series LRC Circuits
Related Practice
Textbook Question
Use a phasor diagram to analyze the RL circuit of FIGURE P32.49. In particular, Find an expression for the crossover frequency ωc.
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Textbook Question
A series RLC circuit consists of a 75 Ω resistor, a 0.12 H inductor, and a 30 μF capacitor. It is attached to a 120 V/60 Hz power line. What is the average power dissipated?
Textbook Question
A series RL circuit is built with a 110 Ω resistor and a 5.0-cm-long, 1.0-cm-diameter solenoid with 800 turns of wire. What is the peak magnetic flux through the solenoid if the circuit is driven by a 12 V, 5.0 kHz source?
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Textbook Question
In FIGURE P32.54, what is the current supplied by the emf when (a) the frequency is very small and (b) the frequency is very large?
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Textbook Question
A series RLC circuit consists of a 50 Ω resistor, a 3.3 mH inductor, and a 480 nF capacitor. It is connected to a 5.0 kHz oscillator with a peak voltage of 5.0 V. What is the instantaneous current i when ε = ε0?
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