Textbook Question
The current in a 2.0 mm x 2.0 mm square aluminum wire is 2.5 A. What are (a) the current density and (b) the electron drift speed?
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Ch 27: Current and Resistance
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 27, Problem 16
A car battery is rated at 90 A h, meaning that it can supply a 90 A current for 1 h before being completely discharged. If you leave your headlights on until the battery is completely dead, how much charge leaves the battery?
Verified step by step guidance1
Understand the relationship between current, time, and charge. The total charge (Q) that flows through a circuit is given by the formula: , where is the charge in coulombs, is the current in amperes, and is the time in seconds.
Convert the time from hours to seconds. Since there are 3600 seconds in an hour, multiply the given time (1 hour) by 3600 to express it in seconds: .
Substitute the given values into the formula. The current is 90 A, and the time is the value you calculated in seconds. The formula becomes: .
Perform the multiplication to find the total charge in coulombs. Remember that 1 ampere-second is equal to 1 coulomb, so the result will be in coulombs.
Interpret the result. The total charge leaving the battery is the product of the current and the time, expressed in coulombs. This value represents the total amount of electric charge that the battery can supply before being completely discharged.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ampere-Hour (A h)
An Ampere-Hour (A h) is a unit of electric charge that represents the amount of charge transferred by a steady current of one ampere flowing for one hour. In the context of a car battery rated at 90 A h, it indicates that the battery can deliver 90 amperes of current for one hour before depletion, which is crucial for understanding battery capacity.
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Charge (Q)
Electric charge, denoted as Q, is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It is measured in coulombs (C), and the total charge that leaves the battery can be calculated by multiplying the current (in amperes) by the time (in hours) the current flows, providing a direct link to the battery's capacity.
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Current (I)
Current (I) is the flow of electric charge in a circuit, measured in amperes (A). It represents the rate at which charge is flowing, and in this scenario, knowing the current drawn by the headlights allows us to determine how long the battery can sustain that current before it is fully discharged, thus linking current to the total charge delivered.
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Related Practice
Textbook Question
What electric field strength is needed to create a 5.0 A current in a 2.0-mm-diameter iron wire?
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Textbook Question
A superconducting magnet carries a 100 A current through a 0.50-mm-diameter superconducting wire that is wound into a coil. How much charge flows through the wire in 15 minutes?
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Textbook Question
A hollow copper sphere has inner radius 1.0 cm and outer radius 2.5 cm. A 5.0 A current flows radially outward from the inner surface to the outer surface. What is the electric field strength at r=2.0 cm?
Textbook Question
A hollow copper wire with an inner diameter of 1.0 mm and an outer diameter of 2.0 mm carries a current of 10 A. What is the current density in the wire?
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Textbook Question
A 0.0075 V/m electric field creates a 3.9 mA current in a 1.0-mm-diameter wire. What material is the wire made of?
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