Assignment 7- Current & Resistance
38 Pages

Assignment 7- Current & Resistance

Course Number: PHYS 2212 ?, Spring 2010

College/University: Georgia State

Word Count: 2890

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Introduction to Electric Current Learning Goal: To understand the nature of electric current and the conditions under which it exists. Electric current is defined as the motion of electric charge through a conductor. Conductors are materials that contain movable charged particles. In metals, the most commonly used conductors, such charged particles are electrons. The more electrons that pass through a cross...

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to Introduction Electric Current Learning Goal: To understand the nature of electric current and the conditions under which it exists. Electric current is defined as the motion of electric charge through a conductor. Conductors are materials that contain movable charged particles. In metals, the most commonly used conductors, such charged particles are electrons. The more electrons that pass through a cross section of a conductor per second, the greater the current. The conventional definition of current is , where is the current in a conductor and is the total charge passing through a cross section of the conductor during the time interval . The motion of free electrons in metals not subjected to an electric field is random: Even though the electrons move fairly rapidly, the net result of such motion is that (i.e., equal numbers of electrons pass through the cross section in opposite directions). However, when an electric field is imposed, the electrons continue in their random motion, but in addition, they tend to move in the direction of the force applied by the electric field. In summary, the two conditions for electric current in a material are the presence of movable charged particles in the material and the presence of an electric field. Quantitatively, the motion of electrons under the influence of an electric field is described by the drift speed, which tends to be much smaller than the speed of the random motion of the electrons. The number of electrons passing through a cross section of a conductor depends on the drift speed (which, in turn, is determined by both the microscopic structure of the material and the electric field) and the crosssectional area of the conductor. In this problem, you will be offered several conceptual questions that will help you gain an understanding of electric current in metals. Part A You are presented with several long cylinders made of different materials. Which of them are likely to be good conductors of electric current? Check all that apply. ANSWER: Introduction to Electric Current Part A Picture 4268 copper Picture 4269 aluminum Picture 4270 glass Picture 4271 quartz Picture 4272 cork Picture 4273 plywood Picture 4274 table salt Picture 4275 gold Correct Part B Metals are good conductors of electric current for which of the following reasons? Introduction to Electric Current Part A ANSWER: Picture 4276 Picture 4277 Picture 4278 Picture 4279 Correct Part C Which of the following is the most likely drift speed of the electrons in the filament of a light bulb? ANSWER: Picture 4280 Picture 4282 Introduction to Electric Current Part C Picture 4284 Picture 4286 Picture 4288 Correct Part D You are presented with several wires made of the same conducting material. The radius and drift speed are given for each wire in terms of some unknown units and . Rank the wires in order of decreasing electron current. Hint D.1 Hint not displayed Hint D.2 Hint not displayed Rank from most to least electron current. To rank items as equivalent, overlap them. ANSWER: http://session.masteringphysics.com/assets/flash/ranking.1196101792.swfhttp://session.masteringphysics.c Introduction to Electric Current Part C Picture 4292 View Correct Part E The drift speed of the electrons in a wire depends strongly on which of the following factors? ANSWER: Picture 4293 the cross-sectional area of the wire Picture 4294 the mass of the wire Picture 4295 the temperature of the wire Picture 4296 the internal electric field in the wire Correct Introduction to Electric Current Part E Part F What quality must the charge density on the surface of a conducting wire possess if an electric field is to act on the negatively charged electrons inside the wire? ANSWER: The charge density must be Picture 4297 Picture 4298 Picture 4299 Picture 4300 Correct A Few Bumps on the Road Learning Goal: To learn to apply the microscopic theory of conduction. A gauge-12 wire has diameter centimeters and length meters. When the voltage volts is applied to the ends of the wire, the current is amperes. The concentration of free electrons in the wire is per cubic meter. Part A Find the resistivity of the wire. Hint A.1 How to approach the problem Hint not displayed Hint A.2 Definition of resistivity Hint not displayed Hint A.3 What is the current density? Hint not displayed Hint A.4 What is the electric field? Hint not displayed Express your answer in ohm-meters. Use two significant figures. Register to View AnswerFew Bumps on the Road Part A = 2.75108 Correct Part B Find the mean time between electron collisions in the wire. Hint B.1 Hint not displayed Hint B.2 Hint not displayed Hint B.3 Definition of resistivity Hint not displayed Express your answer in seconds. Use two significant figures. ANSWER: = 2.201014 Correct A Stretchable Resistor A wire of length and cross-sectional area has resistance . Part A What will be the resistance of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched. Hint A.1 Formula for the resistance of a wire Hint not displayed Hint A.2 Find the cross-sectional area of the stretched wire Hint not displayed Express your answer in terms of the wire's original resistance . ANSWER: = Correct Current in a Wire A metallic wire has a diameter of . When the current in the wire is , the drift Current in a Wire velocity is . Part A What is the density of free electrons in the metal? Hint A.1 How to approach the problem Hint not displayed Hint A.2 Current as a function of concentration of the charge carriers Hint not displayed Express your answer numerically in to two significant figures. ANSWER: 6.951028 Correct Down To The Wire A current of is flowing in a typical extension cord of length . The cord is made of copper wire with diameter . The charge of the electron is . The resisitivity of copper is . The concentration of free electrons in copper is . Part A Find the drift velocity of the electrons in the wire. Hint A.1 Find the current density first Hint not displayed Hint A.2 Current density and the drift speed Hint not displayed Express your answer in meters per second, to two significant figures. ANSWER: = 3.30104 Correct Note that this wire is carrying more current density than is carried by most household wiring in everyday use. With the given amount of current flowing, the cord would be hot to the touch if it were under a rug or had otherwise restricted air flow around it. It would certainly be considered unsafe by Down To The Wire Part A standard electrical safety codes. Even though this wire is carrying a large amount of current for its size, the drift velocity of the electrons is tiny (less than one millimeter per second). This reflects the fact that there is a huge number of free (mobile) electrons in the wire. Let us illustrate this fact with a calculation. Part B The population of the Earth is roughly six billion people. If all free electrons contained in this extension cord are evenly split among the humans, how many free electrons ( ) would each person get? Hint B.1 Hint not displayed Use two significant figures. ANSWER: = 7.501013 All attempts used; correct answer displayed These free electrons undergo frequent collisions with atoms, slowing down and generating heat. How many collisions occur in such a conductor? Let us find out. Part C Find the total number of collisions ( ) that all free electrons in this extension cord undergo in one second. Hint C.1 Consider a single electron How many collisions per second does each electron undergo per second? Hint C.2 Find the time between collisions Down To The Wire Part C Hint C.1 Consider a single electron . Find the algebraic expression for the mean time between collisions Express your answer in terms of , the mass of the electron , the charge of the electron and the concentration of the electrons . ANSWER: = Answer not displayed ANSWER: = 1.801037 Correct Note that does not depend on the applied electric field. The drift speed, however, does. Resistance from Microscopic Ohm's law Your task is to calculate the resistance of a simple cylindrical resistor with wires connected to the ends, such as the carbon composition resistors that are used on electronic circuit boards. Imagine that the resistor is made by squirting material whose conductivity is into a cylindrical mold with length and Resistance from Microscopic Ohm's law cross-sectional area . Assume that this material satisfies Ohm's law. (It should if the resistor is operated within its power dissipation limits.) Part A What is the resistance of this resistor? Hint A.1 General approach Hint not displayed Hint A.2 Microscopic Ohm's law Hint not displayed Hint A.3 Find the voltage from the electric field Hint not displayed Resistance from Microscopic Ohm's law Part A Hint A.4 Find the current from the current density Hint not displayed Hint A.5 Ohm's law for the resistor Hint not displayed Express resistance the in terms of variables given in the introduction. Do not use or in your answer. ANSWER: = Correct Real resistors vary tremendously in overall size. The larger the size, the more power the resistor can dissipate without heating to the point that it is dangerous to nearby components or that the material of which it is constructed begins to change its conductivity (i.e., so that the resistance would no longer be constant). The amount of resistance is determined by the conductivity of the material of the resistor, which can vary over more than 20 orders of magnitude. Commercially available resistors vary from 0.1 ohm or less to more than ohm. The Low-Flow Pipe Learning Goal: To learn to apply and combine the concepts of current, current density, and microscopic Ohm's law. An aluminum "12 gauge" wire has a diameter of 0.205 centimeters. The resistivity of aluminum is ohm-meters. The electric field in the wire changes with time as newtons per coulomb, where time is measured in seconds. Part A Find the current through the conductor at time 5.0 seconds. Hint A.1 How to approach the problem Hint not displayed Hint A.2 The equation for resistance Hint not displayed Express your answer in amperes to two significant figures. ANSWER: = 1.2 Correct Part B Find the charge passing through a cross-section of the conductor between time 0 seconds and time The Low-Flow Pipe Part A 5 seconds. Hint B.1 Hint not displayed Hint B.2 Hint not displayed Express your answer in coulombs to two significant figures. ANSWER: = 2.1 Correct Dependence of Resistance on Resistor Dimensions Ranking Task The rectangular block below has front-face dimensions of 10 by 4 , with a depth of 3 . Dependence of Resistance on Resistor Dimensions Ranking Task You will be asked to treat this object as an electrical resistor. Part A Rank the block based on its electrical resistance along the three illustrated coordinate directions (x, y, and z). Hint A.1 Dependence of resistance on dimensions of resistor Hint not displayed Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER: http://session.masteringphysics.com/assets/flash/ranking.1196101792.swfhttp://session.masteringphysics.c Picture 4368 Dependence of Resistance on Resistor Dimensions Ranking Task Part A View Correct Part B If all of the dimensions of the block double (to become 20 wide, 8 tall, and 6 deep), what happens to the resistance along each axis? Hint B.1 Dependence of resistance on dimensions of resistor Hint not displayed ANSWER: Picture 4372 Picture 4373 Picture 4374 Picture 4375 Picture 4376 Correct Dependence of Resistance on Resistor Dimensions Ranking Task Part A Problem 31.5 electrons flow through a cross section of a square wire in 3.0 . The electron drift speed is . Part A What metal is the wire made of? ANSWER: Picture 4381 Copper Picture 4382 Aluminum Picture 4383 Gold Picture 4384 Silver Correct Problem 31.5 Part A Problem 31.11 The wires leading to and from a 0.12-diameter lightbulb filament are 1.5 in diameter. The wire to the filament carries a current with a current density of . Part A What is the current in the filament? Express your answer using two significant figures. ANSWER: = 0.80 Correct Part B What is the current density in the filament? Express your answer using two significant figures. ANSWER: Problem 31.11 Part A Problem 31.15 The current in an electric hair dryer is 10.0 A. Part A How much charge flows through the hair dryer in 5.0 min? ANSWER: 3000 Correct Part B How many electrons flow through the hair dryer in 5.0 min? ANSWER: Problem 31.21 Part A What is the mean free time between collisions for electrons in silver? ANSWER: 3.801014 Correct s Part B What is the mean free time between collisions for electrons in gold? ANSWER: Problem 31.29 A 1.5 V battery provides 0.50 A of current. Part A At what rate is charge lifted by the charge escalator? ANSWER: 0.500 Correct C/s Part B How much work does the charge escalator do to lift 1.0 C of charge? Problem 31.29 Part A ANSWER: Part C What is the power output of the charge escalator? ANSWER: 0.750 Correct W Problem 31.25 A 0.0075 electric field creates a 3.9 current in a 1.0-diameter wire. Part A What material is the wire made of? ANSWER: Picture 4398 Aluminum Problem 31.25 Part A Picture 4399 Nichrome Picture 4400 Copper Picture 4401 Iron Correct Problem 31.30 Wires 1 and 2 are made of the same metal. Wire 2 has twice the length and twice the diameter of wire 1. What are the ratios (a) of the resistivities and (b) of the resistances of the two wires? Part A ANSWER: 1.00 Correct Part B Problem 31.30 ANSWER: Problem 31.34 Part A How long must a 0.60-mm-diameter aluminum wire be to have a 0.50 A current when connected to the terminals of a 1.5 V flashlight battery? ANSWER: 30.3 Correct m Part B What is the current if the wire is half this length? ANSWER: Problem 31.48 A car battery is rated at , meaning that it can supply a 90 A current for 1 hr before being completely discharged. Part A If you leave your headlights on until the battery is completely dead, how much charge leaves the battery? Express your answer in Coulombs to three significant figures. ANSWER: 3.24105 Correct C Problem 31.51 A hollow metal cylinder has inner radius , outer radius , length , and conductivity . The current is radially outward from the inner surface to the outer surface. Part A Find an expression for the electric field strength inside the metal as a function of the radius from the cylinder's axis. ANSWER: Picture 4411 Problem 31.51 Part A Picture 4413 Picture 4415 Correct Part B Evaluate the electric field strength at the inner surface of an iron cylinder if , and 25 A. ANSWER: Part C Evaluate the electric field strength at the outer surface of an iron cylinder if , and 25 A. Problem 31.51 Part C ANSWER: 1.59104 Correct N/C Problem 31.57 The two wires in the figure are made of the same material. Part A What is the current in the 2.0-mm-diameter segment of the wire? ANSWER: 2.00 Correct A Part B What is the electron drift speed in the 2.0-mm-diameter segment of the wire? Problem 31.57 Part A ANSWER: Problem 31.72 A 5.0-mm-diameter proton beam carries a total current of 1.5 mA. The current density in the proton beam, which increases with distance from the center, is given by , where is the radius of the beam and is the current density at the edge. Part A How many protons per second are delivered by this proton beam? ANSWER: 9.375 Correct Part B Determine the value of . Problem 31.72 Part A ANSWER: Problem 31.27 The two segments of the wire in the figure have equal diameters but different conductivities and . Current passes through this wire. Problem 31.27 Part A If the conductivities have the ratio , what is the ratio of the electric field strengths in the two segments of the wire? ANSWER: Picture 4440 Picture 4442 Picture 4444 Picture 4446 Correct Problem 31.47 The starter motor of a car engine draws a current of 140 from the battery. The copper wire to the motor is 5.40 in diameter and 1.2 m long. The starter motor runs for 0.990 until the car engine Problem 31.47 starts. Part A How much charge passes through the starter motor? ANSWER: 139 Correct C Part B How far does an electron travel along the wire while the starter motor is on? ANSWER: Problem 31.54 The total amount of charge that has entered a wire at time is given by the expression , where is in seconds and . Part A Find an expression for the current in the wire at time . ANSWER: Problem 31.54 Part A Picture 4456 Picture 4458 Picture 4460 Picture 4462 Correct Part B What is the maximum value of the current? Express your answer using two significant figures. ANSWER: Problem 31.61 A 15-cm-long nichrome wire is connected across the terminals of a 1.5 V battery. Part A What is the electric field inside the wire? ANSWER: 10.0 Correct V/m Part B What is the current density inside the wire? ANSWER: Part C If the current in the wire is 2.0 A, what is the wire's diameter? ANSWER: 0.618 Correct mm Problem 31.63 A 1.5 V flashlight battery is connected to a wire with a resistance of 3.00 . The figure shows the battery's potential difference as a function of time. Part A What is the total charge lifted by the charge escalator? ANSWER: 1800 Correct C Problem 31.52 A hollow metal sphere has inner radius , outer radius , and conductivity . The current is radially outward from the inner surface to the outer surface. Problem 31.52 Part A Find an expression for the electric field strength inside the metal as a function of the radius from the center. ANSWER: Picture 4474 Picture 4476 Picture 4478 Picture 4480 Correct Part B Evaluate the electric field strength at the inner surface of a copper sphere if 1.10 ,b 2.60 , and 11.0 . Problem 31.52 Part A ANSWER: Part C Evaluate the electric field strength at the outer surface of a copper sphere if 1.10 ,b 2.60 , and 11.0 . ANSWER: 2.16105 Correct

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UCSD - JAPANESE - JAP10C
JAPN 10C Review of Chapter 1 ( Vol. 2) Lec. Sec. []Name []1. How would you ask for a suggestion or advice when you want to become more skillful at Japanese, but you dont know what to do? 2. What suggestion/advice would you give in the above situation
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 7. Adverbial Use of Adjectives pp.48-49) Lec. Sec. [ ] Name [ ]Review of Adjectives & Adverbs: Adjectives modify nouns. Also, they appear in the latter part of the sentence. prenominal use: The store is selling i
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 6. Admonishment and Prohibition: Lec. Sec. [ ] Name [ pp.45-47)]6.1 (p.46): The following is used to express Admonition or Warning. You must not do ~. plain form: Verb ( TE form) + ( or ) plain form: plain form
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 5. Commands pp.43-44) Lec. Sec. [ 5.1 (p.43): polite command form/ form Verb (]Name []Conjunctive form)= before This fo rm is usually heard/seen in the situations where parents/teachers/authority figures giv
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 4. Conditionals pp.36-37) Lec. Sec. [ ] Name [ ]Review of form: 1. If you are a student, please study. 2. If I were not a student, I would not study. () 3. If the apartment is clean, lets rent it. 4. If the apart
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 3. Saying Whether Something Occurred Before or After: and pp.29-30) Lec. Sec. [ Review (and a new meaning) of and : 1. Ito-sensee is in front]Name []of the blackboard. the table. before the Japanese class. the
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 1. Making a Suggestion pp.18-19) Lec. Sec. [ Review of If ~: If you go to Japan, I think it would be good. Do you think it would be good if I eat sushi? 1.1 (p.18): To ask for a suggestion or advice: Interrogative
UCSD - JAPANESE - JAP10C
(textbook p.124) Refer to How to Write on Jpn Writing Pad at WebC T. Heather Martin one blank box Lec. A at the beginning of each paragraphJapaneseTo look for a word, the following online dictionary may be helpful. http:/ww w.popjisyo.com/ WebHint/Port
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 11. Giving and Receiving pp.92-95) Part III Lec. Sec. [ ] Name [ ]1. 1(bought a present for him)2. 2 (kindly made) (had him make)3. 3(bought a present for him)4. (kindly wrote) 4 (had
UCSD - JAPANESE - JAP10C
JAPN 10C (Grammar and Practice Activities 16. Describing a Preparatory Action: Lec. Sec. [ pp. 117- 118)]Name []1. Isuzu-san drank only water. 2. Suzuki-san did not drink only water. See (p.437 of YOOKOSO Book 1). 3. Toyota-san drank only water (and