1、本單元內容本單元內容9-19-1電位與電容器電位與電容器9-29-2電流與電阻電流與電阻9-39-3電路電路9-1.1 9-1.1 電位能電位能 Fe and Fg are mathematically identical Fe is a conservative force rdFWUUUeif 9-1.2 9-1.2 電位電位 Ue depends on q,but Ve does not qWqUqUqUVVVqUVifif9-1.2 9-1.2 等位面等位面 Four Equipotential Surfaces E.S.for a uniform field,a point char
2、ge,and an electric dipole9-1.3 9-1.3 等位面等位面3 3例例9-1.4 9-1.4 由電場算電位由電場算電位 The differential work done by FfisdEqWsdEqdWsdFdW00,Ex.1 Ex.1 均勻電場均勻電場(a)Along path(a)Ex.1 Ex.1 均勻電場均勻電場路徑路徑(a)(a)EddsEdsEdsEsdEVVfifififiif)0(cosEx.1 Ex.1 均勻電場均勻電場路徑路徑(b)(b)EddEdsEdsEsdEVVfcfifiif222)45(cos9-1.5 9-1.5 點電荷的電位點電
3、荷的電位ffirdEsdEVrdErdEsdE180cosrqVrqrdrqVrqErdEsdEVffffi00202041141441點電荷的電位點電荷的電位點點電電荷荷的的電電位位圖圖9-1.6 9-1.6 一組點電荷的電位一組點電荷的電位 The principle of superposition niiiniirqVV10141(a)on a circle(b)on an arc 0 ,41120EReVEx.2 12 electronsEx.2 12 electrons0 ,41120EReV9-1.7 9-1.7 電雙極的電位電雙極的電位),cos(cos41cos44)(412
4、20200021rrrdrrrprdqrrrrqrqrqVVVVii雙極矩雙極矩 p=p=qdqdlp p 由負電荷指向正電荷由負電荷指向正電荷Induced Dipole Momentl感應雙極矩感應雙極矩l極化極化 (polarization)(polarization)11-4.511-4.5 Polarization(Polarization(偏偏振振)lPolarized LightPolarized LightlThe Plane of PolarizationThe Plane of PolarizationlLinear,Circular and Linear,Circular
5、 and Elliptical Elliptical polarization polarization偏振片偏振片Polarization of LightPolarization of Light偏偏振振與與太太陽陽眼眼鏡鏡水分子與微波爐水分子與微波爐9-1.8 9-1.8 連續電荷分佈的電位連續電荷分佈的電位rdqdVrqVVniiinii010141 41 Line of Charge 2/12200)(4141,dxdxrdqdVdxdqddLLVddLLdxxdxdxdxdxdVVLLL)(ln4ln)(ln4)(ln(4)(4)(412/12202/122002/122002/1
6、22002/1220計計算算)1(2220RzzECharged Disk)(2)(2)()(2(4141)(2(22002/12202/12200zRzRzRdRdVVRzRdRrdqdVRdRdqR計算計算 9-1.9 9-1.9 由電位算電場由電位算電場zVEyVExVEsVEdsdVEdsEqdVqdWzyxs,cos)(cos00 The work done by the electric field Ex.3Ex.3 The charged disk )1(2 )(2)(2220220220RzzzRzdzdzVEzRzVz9-1.109-1.10一組點電荷的電位能一組點電荷的電位
7、能rqqWUrqV210104141 For charges q1 and q2 Ex.4Ex.4 Three charges Ex.5 An alpha particle and a gold nucleus MevfmeeKUK6.2423.9)79)(2(4109-1.119-1.11 Potential of a charged isolated conductor )0(0EsdEVVfiif 導體內部及表面為一等位面導體內部及表面為一等位面(equipotentail surface)DischargePlots of E(r)and V(r)9-1.11 9-1.11 電容器電容
8、器 電容電容（Capacitance）平行板電容器平行板電容器 C=(F 法拉法拉)K:介電常數，真空介電常數，真空=1 0:真空電容率真空電容率 A:板面積板面積 d:兩板距離兩板距離電位差電荷VqC dK0Ex.4Ex.4 1.0 F 電容器 d=1.0mm2281230100101.1 /1085.8100.10.1kmmmFmFCdA9-1.12 9-1.12 Capacitors in Capacitors in parallelparallel等效電容等效電容njjeqeqCCCCCVqCVCCCqqqqVCqVCqVCq1321321321332211)(,9-1.139-1.1
9、3 Capacitors in series Capacitors in series 等效電容等效電容3213213213213322111111/1/1/11)111(,CCCCCCCVqCCCCqVVVVCqVCqVCqVeqeqEx.5Ex.5 A RAM Chipelectrons108.11060.13.5105561915CVFeCVeqnw C=55fF（10-15）V=5.3 volt Ex.6 Ex.6 電容式鍵盤電容式鍵盤Ex.6 Ex.6(cont)A=9.50 10-5m2;k=3.50 按鍵後按鍵後d由由5.00mm減為減為0.150mm 按鍵前按鍵前 C=0.58
10、9PF PFC0.19FPFdk120106.19電電容容式式麥麥克克風風Ex.7Ex.7 defibrillator(除纖顫機除纖顫機)kW100s100.2J200J875)V5000)(F1070(21213262tUPCVU心跳停止病人之急救心跳停止病人之急救 1.1.盡快求助盡快求助2.2.盡快給予先進的救命治療盡快給予先進的救命治療3.3.盡快實行心肺復甦術盡快實行心肺復甦術(CPR)(CPR)4.4.盡快除纖顫盡快除纖顫人體各部位的電位差人體各部位的電位差 人體的肌肉及神經細胞利用鈉、鉀等人體的肌肉及神經細胞利用鈉、鉀等正離子及氯負離子執行生化機能；因正離子及氯負離子執行生化機能
11、；因此造成之電場延伸至人體表面，形成此造成之電場延伸至人體表面，形成小量之電位差。小量之電位差。心電圖心電圖 -電極置於不同位置（電極置於不同位置（A-BA-B，B-CB-C等）即決定不同形狀的心電圖。等）即決定不同形狀的心電圖。腦波圖腦波圖 -電極置於頭部特定部位，紀電極置於頭部特定部位，紀錄電位差隨時間之變化。錄電位差隨時間之變化。心電圖和腦波圖心電圖和腦波圖視網膜電圖視網膜電圖 電流、電流密度與漂移速度電流、電流密度與漂移速度 電阻與電阻率電阻與電阻率 歐姆定律歐姆定律 半導體與超導體半導體與超導體9-2 9-2 電流與電阻電流與電阻9-2.1 9-2.1 電流電流C/s)=A ampe
12、re;(dtdqi 210iii 電荷守恆電荷守恆克希荷夫電流克希荷夫電流(節點節點)定理定理9-2.29-2.2電流密度電流密度AiJJAdAJJdAiAdJiJ:A/mJ:A/m2 2電流密度與漂移速度電流密度與漂移速度dddddvneJneJnAeivnAevvLnALetqivLtenALq)(,=/=,)(銅的漂移速度銅的漂移速度mm/h88.1m/s109.4melectrons/1047.8mass/molmass/matoms/molatoms/mor 732833neJvMNnMNndAA2323262/107.6/105.3/1091.4)2/(mAAiJmAAiJmdAC
13、uCuAlAlAld dAlAl=2.5mm,=2.5mm,d dcucu=1.8mm=1.8mmi=17mA,i=17mA,=9=9 10103 3kg/mkg/m3 3,M=64M=64 1010-3-3kg/mkg/m3 39-2.3 9-2.3 電阻與電阻率電阻與電阻率 Resistance Resistivity Conductivity電阻率電阻率電阻的計算電阻的計算ALRLARAiLVJEAiJLVE/,/溫度效應溫度效應)(000TT nemJEJnemEmeEneJvmeEavmeEmFadd22 ,)(,/,/The effect of temperatureThe eff
14、ect of temperature 電阻的微觀意義電阻的微觀意義effdeffvvsmv)10(/106.1136nem2 nmvseff40105.2149-2.49-2.4 Ohms Law Ohms Law流過一電路元件之流過一電路元件之電流電流與該元件之與該元件之電位差電位差成正比成正比電阻率電阻率與電場的大小及方向無關與電場的大小及方向無關 RViJEI-V curvesconductorpn junction diodeSemiconductorsSemiconductors半導體半導體SuperconductorsSuperconductors超導體超導體More Maglev
15、-magnetic More Maglev-magnetic levitationlevitationhttp:/web.mit.edu/physics/hudson/ResearchBackground.htmMaglevMaglev、MRI and MRI and TevatronTevatronPower line and motorPower line and motorBCS Theory-The Cooper BCS Theory-The Cooper pairspairs9-3 9-3 電路電路 直流電路直流電路 串聯電阻串聯電阻 並聯電阻並聯電阻 交流電路交流電路 虛擬電路實驗
16、虛擬電路實驗9-3.19-3.1直流電路直流電路Direct Current CircuitDirect Current CircuitA bimetallic strip flasherA bimetallic strip flasher以電阻電熱絲加熱以電阻電熱絲加熱bimetallic bimetallic stripstrip，約一秒啟閉一次，可用作警約一秒啟閉一次，可用作警示裝置。示裝置。Ex.8Ex.8 Bimetallic Strip FlasherAutomatic Coffee MakerEx.9 Ex.9 簡單直流電路內之電位（電簡單直流電路內之電位（電壓）升降壓）升降 i
17、RViRVaaEE克希荷夫 Kirchhoff 迴路定理 Ex.10Ex.10 The Ammeter and the VoltmeterEx.11Ex.11 RC電路電路電阻電容電路電阻電容電路Ex.11Ex.11(cont)(cont)Charging a Charging a CapacitorCapacitorRCdtCEqCEqdRCdtCEqdqCEqRCRCqREdtdqRERCqdtdqCqdtdqRdtdqiCqiR)()()()(1,0EEEx.11Ex.11(cont)(cont)?C ist Wha .Const)ln()()(constconstRCtRCtRCteC
18、eeCEqeCEqRCtCEqRCdtCEqCEqdEx.11Ex.11(cont)(cont)RCtRCtRCtRCtRCteRdtdqieCtqCEeCEtqCECeCCEeCCEtq/00)()1()()(0)(EEEx.11 Ex.11(cont)如果如果 R=10MR=10M C=1 C=1 F F經過經過46s46s後，後，e=0.01e=0.01，充電達充電達9999可用作間歇式雨刷等電路控制。可用作間歇式雨刷等電路控制。EECeCtqRC63.0)1()(/1s1010101066FRC9-3.29-3.2 Resistance in series Resistance in
19、seriesnjjeqeqRRRRRRiiRiRiR13213210EEE9-3.39-3.3 Resistors in Resistors in parallel parallel 3213213213322111111)111(,RRRRRiRRRiiiiRiRiRieqeqEEEEEMultiloopMultiloop Circuits Circuitsl The Junction rule:The Junction rule:流入流入接點之電接點之電流必等於流必等於流出流出者者 (Kirchhoffs junction/current(Kirchhoffs junction/curre
20、nt rule)rule)231iiiloopleft 033111RiRiEloopright 022233ERiRiloop big 0222111EERiRi解解System of System of equations(equations(聯立方程聯立方程組組)Ex.12Ex.12 What What are the are the currents?currents?002221321322211111213RiRiRiRiRiRiiiiEEEE解聯立方程組解聯立方程組pivot pivot equatioequation nForward Elimination and Back
21、substitutionpivot equationupper triangle高斯消去法高斯消去法 Ex.13Ex.13 The electric eelThe electric eelThe Equivalent circuitThe Equivalent circuitA106.6140/A93.0093.811401112505000V750500031401iiiiRiRRRRRrRroweqwroweqrowjjeqeproweprowEEEThe currentThe currentR Rw w=800=8009-3.49-3.4交流電路交流電路 Alternating Curr
22、ent CircuitAlternating Current CircuitV(t)=VV(t)=V0 0Sin2Sin2 f t f t f f 頻率頻率 =60H=60H（赫）赫）V V0 0 尖峰值，尖峰值，一般家庭約一般家庭約170V 170V 功率功率P P（t t）=I=I0 0V V0 0SinSin2 2 2 2 f tf t，取時間取時間平均值平均值 對交流電而言，歐姆定律變成對交流電而言，歐姆定律變成 rmsrmsVIVIVIP22210000RIVrmsrmsRVRIVIPrmsrmsrmsrms22Ex.14Ex.14 72W 72W 音箱音箱 VVVVrms24234
23、200.30.824VRVIrmsrmsWVIPrmsrms72Ex.15Ex.15 A practical example Quebec MontrealMW0.55)1000/22.0()A500(MW220)1000/22.0()A1000(368MWV)(500A)1035.7(222,221,5kmmRIPkmmRIPIPavavavE3-way Light BulbElectrical Grounding9-3.59-3.5虛擬電路實驗虛擬電路實驗敬請期待敬請期待磁學磁學(Magnetism)(Magnetism)架設毛髮直豎內部構造http:/www.pnas.org/content/104/34/13565/F5.expansion Negative Temperature Negative Temperature Coefficient of Coefficient of ResistivityResistivity
