Domanda del libro di testo
What is the reactance of a 3.00-H inductor at a frequency of 80.0 Hz?
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Ch 31: Alternating Current
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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TOC.tableOfContents
- 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: 9780321973610Non è quello che usi tu?Cambia libro di testo
Capitolo 31, Problema 15a
You have a 200-Ω resistor, a 0.400-H inductor, and a 6.00-μF capacitor. They are connected to form an L-R-C series circuit. What is the impedance of the circuit?
Guida verificata passo dopo passo1
Step 1: Recall the formula for impedance in an L-R-C series circuit: \( Z = \sqrt{R^2 + (X_L - X_C)^2} \), where \( R \) is the resistance, \( X_L \) is the inductive reactance, and \( X_C \) is the capacitive reactance.
Step 2: Calculate the inductive reactance \( X_L \) using the formula \( X_L = \omega L \), where \( \omega \) is the angular frequency and \( L \) is the inductance. Note that \( \omega = 2\pi f \), where \( f \) is the frequency of the circuit.
Step 3: Calculate the capacitive reactance \( X_C \) using the formula \( X_C = \frac{1}{\omega C} \), where \( C \) is the capacitance and \( \omega \) is the angular frequency.
Step 4: Substitute the values of \( R \), \( X_L \), and \( X_C \) into the impedance formula \( Z = \sqrt{R^2 + (X_L - X_C)^2} \).
Step 5: Simplify the expression to find the impedance \( Z \). Ensure all units are consistent (e.g., convert \( \mu F \) to \( F \) and use SI units for resistance, inductance, and capacitance).
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Impedance in AC Circuits
Impedance is the total opposition that a circuit offers to the flow of alternating current (AC) and is represented as a complex number. It combines resistance (R) and reactance (X), where reactance arises from inductors and capacitors. The formula for impedance in an L-R-C series circuit is Z = √(R² + (X_L - X_C)²), where X_L is the inductive reactance and X_C is the capacitive reactance.
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Percorso guidato
08:40
Impedance in AC Circuits
Inductive Reactance
Inductive reactance (X_L) is the opposition to the change of current in an inductor and is given by the formula X_L = 2πfL, where f is the frequency of the AC source and L is the inductance in henries. This reactance increases with frequency, meaning that at higher frequencies, inductors resist changes in current more strongly, affecting the overall impedance of the circuit.
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Percorso guidato
12:59Mutual Induction
Capacitive Reactance
Capacitive reactance (X_C) is the opposition to the change of voltage across a capacitor and is calculated using the formula X_C = 1/(2πfC), where C is the capacitance in farads. Unlike inductive reactance, capacitive reactance decreases with increasing frequency, which means that capacitors allow more current to pass at higher frequencies, influencing the total impedance in the circuit.
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Percorso guidato
08:02Capacitors & Capacitance (Intro)
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