Lecture 6. Previous Lecture. Capacitors C. Capacitors in series Capacitors in parallel E stored in an E field

Transcription

1 Lecture 6 Previous Lecture Q Capacitors C V Capacitors in series Capacitors in parallel E stored in an E field 1 1 = = C C Δ series parallel This Lecture Current Resistivity as a property of materials Emf 1 C i i i = C 1 1 PEcap = QΔ V uelec = ε0e 2 2 i 2

2 Exam 1(Monday Feb. 4, 8:00-9:30 PM) *Location STEW 183 *Covers all readings, lectures, homework from Chapters 17 through 19.4 *The exam will be multiple choice and is meant to be done within 60 minutes by a well-prepared student. We will give 90 minutes starting promptly at the listed time, so please be on time! Be sure to bring your student ID card, calculator, pencil and your own onepage (two-side) crib sheet. NOTE THAT FEW EQUATIONS WILL BE GIVEN YOU ARE REMINDED THAT IT IS YOUR RESPONSIBILITY TO CREATE WHATEVER TWO-SIDED CRIB SHEET YOU WANT TO BRING TO THIS EXAM. 1/27/13 2

3 ILQ 1 Currently, Physics 221 help center is open on M and F only. Would you prefer to re-schedule the help center instructors from M and F to other days of the week (T, W, and Th)? The total number of available help hours per week would not change. A: YES, open the help center on (T, W, and Th), but reduce available hours on M and F. B: NO, keep the help center opened on M and F only. 3

4 Electrostatics versus Electric Current Conductors have free electrons moving at ~10 6 m/s. Electrons bump into the fixed positive nuclei random paths. On average no net displacement of charge no current 4

5 Electric Current Electrostatic Equilibrium Steady-State + - Battery Current is defined as the rate of flow of charge through an area. ΔQ I = Δt SI unit for I is the ampere (A). 1A = 1C s Convention: Current arrow is drawn in direction in which positive charge carriers would move, even if the actual charges are negative & move in the opposite direction. 5

6 Electric Current Notice that flow of positive charge in one direction, Becomes more negative Becomes more positive CURRENT I Equivalent to negative charge in opposite direction. Becomes more negative CURRENT I Becomes more positive

7 Drift Velocity In an electric field there is a drift along a preferred direction. With without E E Drift velocity = average speed of electrons DC Current: net flow through a surface 7

8 Drift Speed, Total Charge & Current # charge carriers n = volume q = charge of each particle v d = drift velocity In time Δt, all N particles in volume Av d Δt pass through area A: N = nav d Δt The total charge passing through A is: Q = qnav d Δt ΔQ Δt = qnav d = I 8

9 Relationship between Current and Drift Speed Find v d for 14-gauge copper wire carrying a current of 1 A. Assume there is 1 free electron/atom. Must find n =number of charged carriers/ V n = ρn M v d = I qna Copper ρ = 8.93 g/cm 3 M = g/mol 14 gauge wire A 2.081mm 2 9

10 Relationship between Current and Drift Speed Find v d for 14-gauge copper wire carrying a current of 1 A. Assume there is 1 free electron/atom. v d = I qna 19 Electrons are the carriers q= e= C C 1 I s vd = = qna ( C) ( m ) mm 6 v m d = = 35.4 µ m/s s Copper ρ = 8.93 g/cm 3 M = g/mol 14 gauge wire A 2.081mm 2 1 m 1000 mm An electron takes hours to travel 1 meter. 2 10

11 Electric Current one q in one q out A copper wire behaves like a full water hose. The wire is full of electrons. If the motion of charge starts at one end of the wire, then the other end reacts to this motion. This is like a full water hose Turn on the H 2 O pressure and water comes out immediately. The pressure wave travels much faster than an H 2 O molecule. 11

12 Resistance Resistance is a property of the object, i.e. It depends on the shape and material V =V a V b = E ΔL R = V I SI unit for resistance R : ohm (Ω) 1 Ω =1V / A Ohm s Law Ohmic materials (e.g., most metals): R is constant. Nonohmic materials: R constant 12

13 Resistance & Ohm s Law ohmic Non-ohmic 13

14 Resistivity Resistivity ( ρ) is a property of the material. area A I L I length R = ρ L A SI unit for ρ : ohm - meter (Ω m) Resistivity ρ depends on temperature. Usually the resistivity is given at T=20 o C. 14

15 ILQ 2 A metal rod has a length L, an area A, and an original resistance of R = 1Ω. The rod is then extruded to a final length 2L (and area A/2). What is the final resistance? (A) 1Ω (B) 2Ω (C) 4Ω 15

16 Resistivity & Temperature Coefficients Material Resistivity ρ (Ωm) 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, n-type 8.7 x 10-4 Si, p-type 2.8 x 10-3 glass

17 Temperature Dependence ρ for copper (Cu) as a function of temperature Notice: Resisitivity increases as temperature increases. This curve does not deviate greatly from a straight line. 17

18 DEMO: Temperature Dependence liquid nitrogen ~ 77 o K Lower Cu initially at room temperature (~ 300 o K) into liquid N 2. vacuum bottle 18

19 DEMO: Temperature Dependence lamp B Heat the Ge with a candle. S semiconductor Ge 19

20 Real Battery internal resistance emf In an ideal battery: r = 0 V a V b = ε I = V R Examine potential as we start from point b and end at a: ε Ir IR = 0 I = Note: ε arrows always points from negative to positive. ε R + r Over the battery: V a V b = ε Ir 20

21 Effect of Internal Resistance r =0 (ideal battery) real battery 21

22 ILQ3 A human being can be electrocuted if a current as small as 50 ma passes near the heart. An electrician working with sweaty hands makes good contact with the two conductors that he is holding. If his resistance is 2000 Ω, which of the following might be the fatal voltage? (A) 100 V (B) (C) (D) 10 V 1 V 0.1 V (E) 0.01 V 22

23 Power P in electrical circuits When current flows through a resistance R, Joule heating occurs. ΔU = V ΔQ ΔU Δt = V ΔQ Δt = VI P = IV = I 2 R = V 2 R 23