Lecture 7.1 : Current and Resistance

Transcription

1 Lecture 7.1 : Current and Resistance Lecture Outline: Current and Current Density Conductivity and Resistivity Resistance and Ohm s Law Textbook Reading: Ch Feb. 26,

2 Announcements By popular demand...no new Homework assignment this week. Exam #2 Thu. (Feb. 28) in class. Covers Ch Review session for Exam #2 is scheduled for Wed., Feb. 27, from 7-9pm in Stolkin. Bring your clickers. Do not wait for this review session to begin your exam preparations! 2

3 Last Lecture... Conduction electrons are like free particles moving through a metal lattice. No Electric Field Average Velocity is Zero With Electric Field Average Velocity is NonZero 3

4 Last Lecture... Electrons are the charge carriers in metals! electron current (i e ) = number of electrons per second that pass through a conductor in a given time. i e = n e Aν d = n eeτa m E 4

5 Current and Current Density Current was known long before electrons were discovered, so conventional definition of current is in terms of Charge: I dq dt 1 ampere = 1 A 1 coulomb per second = 1 C/s Conventional current and electron current are related: I = Q t = en e t = ei e 5

6 Current and Current Density By convention, current is defined to flow in the direction in which positive charges would move! (i.e. - in the direction of the Electric Field) 6

7 Current and Current Density We define current density (J) to arrive at a property intrinsic to a material, and not specific to the cross-sectional Area of a conductor. J I A = n eeν d The current in a 100 Watt lightbulb is 0.85 A. The filament inside the bulb is 0.25 mm in diameter. What is the current density in the filament? 7

8 Current and Current Density Current is a conserved quantity! The current is the same at all points in a current-carrying wire. Current is not used up by the paddle...but energy is required to turn the paddle. 8

9 Current and Current Density A and B are identical lightbulbs connected to a battery as shown. Which is brighter? A. Bulb A. B. Bulb B. C. The bulbs are equally bright. 9

10 Current and Current Density Kirchoff s Junction Law: Iin = I out Current =? 10

11 Conductivity and Resistivity J = n e eν d = n e e eτe m = n ee 2 τ m E Define a new property of materials σ = conductivity = n ee 2 τ m J = σe Conductivity describes how easily electrons can move through a material. (Also depends on temperature) 11

12 Conductivity and Resistivity Inverse of conductivity (resistivity) tells how reluctant electrons are to move through a material. ρ =resistivity= 1 σ = m n e e 2 τ 12

13 Conductivity and Resistivity Superconductivity! Some materials exhibit zero resistance to current if they are cooled to low enough temperatures. 13

14 Conductivity and Resistivity A 3.0 mm diameter wire carries a 12 A current when the electric field is V/m. What is the wire s resistivity? 14

15 Resistance and Ohm s Law Potential Difference across conductor creates Electric field. E = V s = V L I = JA = AσE = A ρ E Ohm s Law: I = A ρl V V R R = resistance 15

16 Resistance and Ohm s Law Resistance (R) characterizes ability of current to flow through specific piece of conductor with a specific geometry. R = ρl A 1 ohm = 1 Ω 1 Volt/Ampere = 1 V/A Wire 2 is twice the length and twice the diameter of wire 1. What is the ratio R 2 /R 1 of their resistances? 16

17 Resistance and Ohm s Law Ohm s Law: Establishing a potential difference ΔV across the ends of a conductor with resistance R causes a current I through the current. I = V R Example: What resistor would have a 15 ma current if connected across the terminals of a 9.0 V battery? 17

18 Resistance and Ohm s Law In this course, we will assume wires are ideal (R = 0 Ω ), so they don t have any potential drop across them. Real wires have some resistance, and use up some energy in a circuit. 18

19 Resistance and Ohm s Law Resistors are placed in electrical circuits to control the voltage at different points in the circuit. Resistors are made out of materials, such as carbon, that are poor conductors. 19

20 Reminders Exam #2 Thursday (Feb. 28). Bring a calculator and your 1 sheet of notes. All problems assigned during recitations are fair game for exams! 20