Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 31. Current and Resistance Lights, sound systems, microwave ovens, and computers are all connected by wires to a battery or an electrical outlet. How and why does electric current flow through a wire? Chapter Goal: To learn how and why charge moves through a conductor as what we call a current.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Topics: The Electron Current Creating a Current Current and Current Density Conductivity and Resistivity Resistance and Ohm’s Law Chapter 31. Current and Resistance

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 31. Reading Quizzes

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What quantity is represented by the symbol J ? A. Resistivity B. Conductivity C. Current density D. Complex impedance E. Johnston’s constant

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. Resistivity B. Conductivity C. Current density D. Complex impedance E. Johnston’s constant What quantity is represented by the symbol J ?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electron drift speed in a typical current-carrying wire is A.extremely slow (≈10 –4 m/s). B.moderate (≈ 1 m/s). C.very fast (≈10 4 m/s). D.Could be any of A, B, or C. E.No numerical values were provided.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.extremely slow (≈10 –4 m/s). B.moderate (≈ 1 m/s). C.very fast (≈10 4 m/s). D.Could be any of A, B, or C. E.No numerical values were provided. The electron drift speed in a typical current-carrying wire is

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. All other things being equal, current will be larger in a wire that has a larger value of A.conductivity. B.resistivity. C.the coefficient of current. D.net charge. E.potential.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. All other things being equal, current will be larger in a wire that has a larger value of A.conductivity. B.resistivity. C.the coefficient of current. D.net charge. E.potential.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The equation I = ∆V/R is called A. Ampère’s law. B. Ohm’s law. C. Faraday’s law. D. Weber’s law.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The equation I = ∆V/R is called A. Ampère’s law. B. Ohm’s law. C. Faraday’s law. D. Weber’s law.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 31. Basic Content and Examples

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

The Electron Current Pushing on the sea of electrons with an electric field causes the entire sea of electrons to move in one direction like a gas or liquid flowing through a pipe. This net motion, which takes place at the drift speed v d, is superimposed on top of the random thermal motions of the individual electrons. The electron current is the number of electrons per second that pass through a cross section of a wire or other conductor. n e is the number density of electrons. The electron current in a wire of cross-sectional area A is

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.1 The size of the electron current QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.1 The size of the electron current

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.1 The size of the electron current

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Creating a Current The average speed at which the electrons are pushed along by an electric field is Where τ is the mean time between collisions, and m is the mass of the electron. The electron current is then

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.3 The electron current in a copper wire QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.3 The electron current in a copper wire

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.3 The electron current in a copper wire

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.3 The electron current in a copper wire

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Current If Q is the total amount of charge that has moved past a point in a wire, we define the current I in the wire to be the rate of charge flow: The SI unit for current is the coulomb per second, which is called the ampere. 1 ampere = 1 A = 1 C/s. The conventional current I and the electron current i e are related by

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.4 The current in a copper wire QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.4 The current in a copper wire

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

The Current Density in a Wire The current density J in a wire is the current per square meter of cross section: The current density has units of A/m 2.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Kirchhoff’s Junction Law For a junction, the law of conservation of current requires that where the Σ symbol means summation. This basic conservation statement – that the sum of the currents into a junction equals the sum of the currents leaving – is called Kirchhoff’s junction law.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Conductivity and Resistivity The conductivity of a material is Conductivity, like density, characterizes a material as a whole. The current density J is related to the electric field E by: The resistivity tells us how reluctantly the electrons move in response to an electric field:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 31.7 Mean time between collisions QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.7 Mean time between collisions

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Resistance and Ohm’s Law The resistance of a long, thin conductor of length L and cross=sectional area A is The SI unit of resistance is the ohm. 1 ohm = 1 Ω = 1 V/A. The current through a conductor is determined by the potential difference ΔV along its length:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.8 The current in a nichrome wire QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.8 The current in a nichrome wire

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.8 The current in a nichrome wire

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Ohm’s Law Ohm’s law is limited to those materials whose resistance R remains constant—or very nearly so—during use. The materials to which Ohm’s law applies are called ohmic. The current through an ohmic material is directly proportional to the potential difference. Doubling the potential difference doubles the current. Metal and other conductors are ohmic devices.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 31.9 A battery and a resistor QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 31.9 A battery and a resistor

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 31. Summary Slides

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 31. Clicker Questions

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. These four wires are made of the same metal. Rank in order, from largest to smallest, the electron currents i a to i d. A. i d > i a > i b > i c B. i b = i d > i a = i c C. i c > i b > i a > i d D. i c > i a = i b > i d E. i b = i c > i a = i d

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. These four wires are made of the same metal. Rank in order, from largest to smallest, the electron currents i a to i d. A. i d > i a > i b > i c B. i b = i d > i a = i c C. i c > i b > i a > i d D. i c > i a = i b > i d E. i b = i c > i a = i d

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Why does the light in a room come on instantly when you flip a switch several meters away? A.Electrons travel at the speed of light through the wire. B.Because the wire between the switch and the bulb is already full of electrons, a flow of electrons from the switch into the wire immediately causes electrons to flow from the other end of the wire into the lightbulb. C.The switch sends a radio signal which is received by a receiver in the light which tells it to turn on. D.Optical fibers connect the switch with the light, so the signal travels from switch to the light at the speed of light in an optical fiber.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Why does the light in a room come on instantly when you flip a switch several meters away? A.Electrons travel at the speed of light through the wire. B.Because the wire between the switch and the bulb is already full of electrons, a flow of electrons from the switch into the wire immediately causes electrons to flow from the other end of the wire into the lightbulb. C.The switch sends a radio signal which is received by a receiver in the light which tells it to turn on. D.Optical fibers connect the switch with the light, so the signal travels from switch to the light at the speed of light in an optical fiber.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The two charged rings are a model of the surface charge distribution along a wire. Rank in order, from largest to smallest, the electron currents E a to E e at the midpoint between the rings. A. E c > E e > E a > E b = E d B. E d > E b > E e > E a = E c C. E c = E d > E e > E a = E b D. E b = E d > E a = E c = E e E. E a = E b > E e > E c = E d

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The two charged rings are a model of the surface charge distribution along a wire. Rank in order, from largest to smallest, the electron currents E a to E e at the midpoint between the rings. A. E c > E e > E a > E b = E d B. E d > E b > E e > E a = E c C. E c = E d > E e > E a = E b D. E b = E d > E a = E c = E e E. E a = E b > E e > E c = E d

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What are the magnitude and the direction of the current in the fifth wire? A.15 A into the junction B.15 A out of the junction C.1 A into the junction D.1 A out of the junction E.Not enough data to determine

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.15 A into the junction B.15 A out of the junction C.1 A into the junction D.1 A out of the junction E.Not enough data to determine What are the magnitude and the direction of the current in the fifth wire?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Rank in order, from largest to smallest, the current densities J a to J d in these four wires. A. J c > J b > J a > J d B. J b > J a = J d > J c C. J b > J a > J c > J d D. J c > J b > J a = J d E. J b = J d > J a > J c

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. J c > J b > J a > J d B. J b > J a = J d > J c C. J b > J a > J c > J d D. J c > J b > J a = J d E. J b = J d > J a > J c Rank in order, from largest to smallest, the current densities J a to J d in these four wires.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A wire connects the positive and negative terminals of a battery. Two identical wires connect the positive and negative terminals of an identical battery. Rank in order, from largest to smallest, the currents I a to I d at points a to d. A. I c = I d > I a > I b B. I a = I b > I c = I d C. I c = I d > I a = I b D. I a = I b = I c = I d E. I a > I b > I c = I d

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. I c = I d > I a > I b B. I a = I b > I c = I d C. I c = I d > I a = I b D. I a = I b = I c = I d E. I a > I b > I c = I d A wire connects the positive and negative terminals of a battery. Two identical wires connect the positive and negative terminals of an identical battery. Rank in order, from largest to smallest, the currents I a to I d at points a to d.