Textbook Question
In FIGURE EX28.30, what is the value of the potential at points 1 and 2?
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Ch 28: Fundamentals of 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 28, Problem 34
What is the time constant for the discharge of the capacitors in FIGURE EX28.34?
Verified step by step guidance1
Identify the formula for the time constant \( \tau \) in an RC circuit, which is given by \( \tau = R \cdot C \), where \( R \) is the equivalent resistance and \( C \) is the capacitance.
Determine the equivalent resistance \( R_{eq} \) of the circuit. If the resistors are in series, add their resistances directly: \( R_{eq} = R_1 + R_2 + \dots \). If they are in parallel, use the formula \( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots \).
Determine the total capacitance \( C_{eq} \) of the circuit. If the capacitors are in series, use the formula \( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots \). If they are in parallel, add their capacitances directly: \( C_{eq} = C_1 + C_2 + \dots \).
Substitute the values of \( R_{eq} \) and \( C_{eq} \) into the formula \( \tau = R_{eq} \cdot C_{eq} \) to calculate the time constant.
Verify the units of the time constant \( \tau \). The resistance \( R \) is in ohms (\( \Omega \)) and the capacitance \( C \) is in farads (F), so \( \tau \) will be in seconds (s).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Capacitance
Capacitance is the ability of a capacitor to store charge per unit voltage. It is measured in farads (F) and is defined by the formula C = Q/V, where C is capacitance, Q is the charge stored, and V is the voltage across the capacitor. Understanding capacitance is essential for analyzing how capacitors behave in circuits, especially during charging and discharging processes.
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Capacitors & Capacitance (Intro)
Time Constant
The time constant, denoted by the symbol τ (tau), is a measure of the time it takes for a capacitor to charge to about 63.2% of the maximum voltage or to discharge to about 36.8% of its initial voltage. It is calculated using the formula τ = RC, where R is the resistance in ohms and C is the capacitance in farads. The time constant is crucial for understanding the speed of the charging and discharging processes in RC circuits.
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RC Circuit
An RC circuit is an electrical circuit that consists of a resistor (R) and a capacitor (C) connected in series or parallel. The behavior of the circuit during charging and discharging is governed by the time constant, which influences how quickly the capacitor can store or release energy. Analyzing RC circuits is fundamental in electronics, particularly in timing applications and signal processing.
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Related Practice
Textbook Question
It seems hard to justify spending \$5.00 for an LED lightbulb when an ordinary incandescent bulb costs 50¢. To see if this makes sense, compare a 60 W incandescent bulb that lasts 1000 hours to a 10 W LED bulb that has a lifetime of 15,000 hours. Both bulbs produce the same amount of visible light. If electricity costs \$0.15/kWh, what is the total cost—purchase price plus energy—to get 15,000 hours of light from each type of bulb? This is called the life-cycle cost.
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Textbook Question
Show that the product RC has units of s.
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Textbook Question
What is the equivalent resistance between points 1 and 2 in FIGURE EX28.27?
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Textbook Question
A capacitor is discharged through a 100 Ω resistor. The discharge current decreases to 25% of its initial value in 2.5 ms. What is the value of the capacitor?
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Textbook Question
An electric eel develops a 450 V potential difference between its head and tail. The eel can stun a fish or other prey by using this potential difference to drive a 0.80 A current pulse for 1.0 ms. What are (a) the energy delivered by this pulse and (b) the total charge that flows?
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