Domanda del libro di testo
The switch in FIGURE P30.76 has been open for a long time. It is closed at t = 0 s. What is the current through the 20 Ω resistor after the switch has been closed a long time?
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Ch 30: Electromagnetic Induction
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 30, Problema 76a
The switch in FIGURE P30.76 has been open for a long time. It is closed at t = 0 s. What is the current through the 20 Ω resistor immediately after the switch is closed?
Guida verificata passo dopo passo1
Step 1: Analyze the circuit configuration. The circuit consists of a 30 V battery, a 10 Ω resistor, a 20 Ω resistor, and a 10 mH inductor. The switch has been open for a long time, meaning the inductor has no initial current flowing through it. When the switch is closed at t = 0 s, the inductor will oppose any sudden change in current due to its inductive property.
Step 2: Understand the behavior of the inductor immediately after the switch is closed. At t = 0 s, the inductor behaves like an open circuit because it resists any instantaneous change in current. Therefore, no current flows through the branch containing the inductor at this instant.
Step 3: Simplify the circuit for t = 0 s. Since the inductor acts as an open circuit, the 20 Ω resistor is effectively disconnected from the circuit. The current flows only through the 10 Ω resistor connected directly to the battery.
Step 4: Apply Ohm's Law to calculate the current through the 10 Ω resistor. The voltage across the resistor is equal to the battery voltage (30 V). Using Ohm's Law, \( I = \frac{V}{R} \), where \( V \) is the voltage and \( R \) is the resistance.
Step 5: Conclude that the current through the 20 Ω resistor is zero immediately after the switch is closed because the inductor prevents current from flowing through its branch at t = 0 s.
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Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Ohm's Law
Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed mathematically as I = V/R. Understanding this law is crucial for calculating the current through resistors in a circuit.
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Percorso guidato
03:07
Resistance and Ohm's Law
Inductance and Inductive Reactance
Inductance is a property of an electrical component, typically a coil or inductor, that opposes changes in current. When the switch is closed, the inductor initially resists the change in current, creating a transient response. The inductive reactance (XL) can be calculated using the formula XL = 2πfL, where f is the frequency and L is the inductance. However, immediately after closing the switch, the inductor behaves like a short circuit.
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Percorso guidato
12:59Mutual Induction
Transient Response in RL Circuits
In an RL circuit, when a switch is closed, the current does not instantly reach its maximum value due to the inductor's opposition to changes in current. Instead, the current increases gradually, following an exponential curve characterized by the time constant τ = L/R, where L is the inductance and R is the total resistance in the circuit. Analyzing the transient response is essential for understanding the behavior of the circuit immediately after the switch is closed.
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Percorso guidato
07:50LR Circuits
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