9/22/16 ANNOUNCEMENT ANNOUNCEMENT FINAL EXAM

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1 ANNOUNCEMENT Exam 1: Tuesday September 27, 2016, 8 PM 10 PM Location: Elliot Hall of Music Covers all readings, lectures, homework from Chapters 21 through 23 Multiple choice (1518 questions) Practice exams On the course website and on CHIP Bring your student ID card and your own onepage (twosides) crib sheet Only a few equations will be given The equation sheet that will be given with the exam is posted on the course homepage Link on the right labeled Equationsheet It is your responsibility to create your own crib sheet Crib sheet 8.5 x 11 ANNOUNCEMENT Can be handwritten, computergenerator, painted, etc. All calculators allowed Except webenabled, internet or bluetooth connected Nothing that can communicate with other devices FINAL EXAM When: Wednesday December 14, PM 9 PM Location: Elliot Hall of Music Details to come 1

2 9/22/16 Chapter 25 Electric Current and DC Circuits Current Resistivity as a property of materials Temperature dependence of resistivity EMF Power Electrostatics vs. Electric Current Electrostatics: charges at rest Conductors have free electrons moving at ~106 m/s Bump into fixed positive nuclei Follow weird random paths No net displacement of charge on average Electric current: net transport of charge through a given surface Electric Current Electrostatic Equilibrium SteadyState Current Battery Current (I) = rate of flow of charge through an area SI unit = Ampere (A) (C/s) I= ΔQ Direction represented by the flow of positive charge Historical reasons Negative charges (electrons) actually move in conductors 2

3 Electric Current Flow of positive charge in one direction Becomes more negative Becomes more positive CURRENT I Flow of negative charge in the opposite direction Completely equivalent! Becomes more negative Becomes more positive CURRENT I Drift Velocity In electric field Electrons move in preferred direction on average = Drift Can be represented by an average speed Neglecting collisions Average speed = drift velocity Steady current: Net flow through a surface Microscopic View of Electron Motion No! E! E With! E 3

4 Drift Speed, Total Charge & Current # charge carriers n = volume q = charge of each particle v d = drift velocity In time, all N particles in volume Av d pass through area A N = nav d Total charge passing through A ΔQ = qnav d ΔQ = I = qnav d Relationship Between I and v d Find v d for 14gauge copper wire carrying a current of 1 A. Assume there is 1 free electron/atom. I = qnav Copper d v d = I qna ρ = 8.93 g/cm 3 n = n atoms = ρn Avogadro M g 8.93 n = cm 3 atoms g mol mol atoms n = cm cm 3 1m n = atoms m 3 3 M = g/mol 14 gauge wire Area = mm 2 Relationship Between I and v d Find v d for 14gauge copper wire carrying a current of 1 A. Assume there is 1 free electron/atom. I = qnav Copper d v d = I qna ρ = 8.93 g/cm 3 v d = I qna = q = e = C 1 C s ( C) ( m 3 ) mm 2 v d = m s = 35.5 µ m/s Would take 1 e hours to go 1 m! M = g/mol 14 gauge wire Area = mm m 1000 mm How do lights come on instantaneously when we flip a switch? 4

5 Electric Current one q in one q out Copper wire much like a full water hose Wire full of electrons Water hose full of water Motion of charge starts at one end of the wire The other end immediately reacts Turn on water Immediately comes out Pressure wave travels much faster than a H 2 O molecule Resistance V =V a V b = E ΔL R V I (Ohm's Law) Resistance is a property of the object Depends on the shape and material SI unit for R = ohm (Ω) 1 Ω = V/A Ohmic materials (e.g., most metals) Constant R Nonohmic materials Variable R Resistance & Ohm s Law Ohmic NonOhmic 5

6 Resistivity area A I L I R = ρ L A length Resistivity (ρ) is a basic material property SI unit: ohmmeter (Ωm) Temperaturedependent Resistivity & Temperature Coefficients Material Resistivity ρ (Ωm) (20 C) Temp. coeff. α (K 1 ) Ag 1.6 x x 10 3 Cu 1.7 x x 10 3 W 5.5 x x 10 3 Si x 10 2 Si, ntype 8.7 x 10 4 Si, ptype 2.8 x 10 3 glass ( α = ρ ρ 0) ρ 0 ) semiconductors insulator See TM Table 251 for more Temperature Dependence of ρ and R ( ) Temperature coefficient of ρ Multiply both sides by ρ 0 (TT 0 ) ρ 0 )α = ρ ρ 0 α = ρ ρ 0 ρ 0 ) Solve for ρ Since R = ρl/a Heated Tungsten Light Bulb filament at 3000 K: α = 4.5x10 3 / K ρ = ρ 0 1α ) R = R 0 1α ) ( ) R 3000 = R x K 293K R 3000 = 13.2R 20 6

7 Temperature Dependence ρ for copper (Cu) as f(t) Resisitivity increases as temperature increases Approximately linear Demo Temperature Dependence of ρ liquid nitrogen ~ 77 o K Lower Cu initially at room temperature (~ 300 K) into liquid N 2 vacuum bottle Demo Temperature Dependence lamp B Heat the Ge with a candle S semiconductor Ge 7

8 TemperatureStable Resistor A temperaturestable resistor is to be made by connecting a resistor made of Si in series with one made of NiChrome. If the required total resistance is 1300 Ω in a wide temperature range around 20ºC, what should the resistances of the two resistors be? R total = R N R Si = 1300Ω In general: R = R 0 (1α )) R n R Si R 0N (1 )) R 0Si (1 )) = 1300Ω (R 0N R 0Si ) R 0N ) R 0Si )) = 1300Ω (R 0N R 0Si ) (R 0N R 0Si ) ) = 1300Ω (R 0N R 0Si ) ) = 0 To eliminate temperature dependence Temperature Stable Resistor A temperaturestable resistor is to be made by connecting a resistor made of Si in series with one made of NiChrome. If the required total resistance is 1300 Ω in a wide temperature range around 20ºC, what should the resistances of the two resistors be? R total = R N R Si = 1300Ω In general: R = R 0 (1α )) R n R Si (R 0N R 0Si ) ) = 0 To eliminate temperature dependence (R 0N R 0Si ) = 0 (1300Ω R 0Si ) R 0Si = 0 R 0N R 0Si = 1300Ω R 0N = 1300Ω R 0Si 1300Ω R 0Si R 0Si = 0 R 0Si = 1300Ω Power in Electric Circuits When current flows through a resistance R, kinetic energy gain dissipated as heat = Joule heating ΔU = (V a V b )ΔQ =VΔQ ΔU =V ΔQ =VI P = IV = I 2 R = V 2 R Units: VA = J/s = Watt (W) 8

9 EMF (ξ): Electromotive force Not actually a force Another name for potential difference r : Internal resistance Ideal Battery In an ideal battery, potential from b to a r = 0 V a V b =V = ξ I = ξ R Note: ξ arrows always point from to EMF (ξ): Electromotive force Not actually a force Another name for potential difference r : Internal resistance Real Battery In a real battery, potential from b to a Can model as ideal battery small resistor V a V b = ε Ir For large I, terminal voltage drops ξ Ir IR = 0 I = ξ R r Effect of Internal Resistance r =0 (Ideal battery) Real battery 9

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