ShortVersion24.ElectricCurrent短版24.电流

1、Short Version : 24. Electric Current 短版: 24. 電流24.1. Electric Current電流Current (I) = Net rate of (+) charge crossing an area. 電流 (I) = 通過一面積的淨(+)電荷速率。 I = Ampere 安培Electronics : I mA 電子器材Biomedics : I A生物醫學器材Steady current:穩定電流QItInstantaneous current:瞬間電流d QId t+ charges moving right+ 電荷往右走- charge

2、s moving left- 電荷往左走Both charges moving right兩種電荷都往右走Net current淨電流淨電流Zero net current無淨電流無淨電流Curent: A Microscopic Look電流：微觀看法v of charge carriers in media with E = 0 is thermal ( random with v = 0 ).在 E = 0 介質中，電荷載子的 v 來自熱 ( 隨機： v = 0 )For E 0, vd = v 0. drift velocity漂移速度QIt/dn A L qL vn = number

3、 of carriers per unit volume單位體積內電荷載子的數目q = charge on each carrier每個載子的電荷Charge in this volume is Q = n A L q. 這體積內的電荷是dIn A q vExample 24.1. Copper Wire銅線A 5.0-A current flows in a copper wire with cross-sectional area 1.0 mm2,一個 5.0-A 電流在一條截面積為 1.0 mm2 的銅線內流動， carried by electrons with number dens

4、ity n = 1.11029 m-3.載子是密度 n = 1.11029 m-3 的電子。Find the electrons drift speed.求電子的漂移速率。dIvn A q29362195.01.1 101.0 101.6 10-AmmC42.8 10/-m s0.28/mm s TIP : Big difference between vd mm/s and signal speed c.提示： vd mm/s 與訊號的速率 c 有甚大差別。Current Density電流密度Current can flow in ill-defined paths ( vd depend

5、s on position ),電流可以順着不甚明確的路徑流動 ( vd 隨位置而異 ) ， e.g., in Earth, chemical solutions, ionized gas, 例： 地球，化學溶液，電離氣體，Better description of such flows is by描述這些電流最好用current density ( J ) = current per unit area 電流密度 ( J ) = 單位面積的電流dn qJv J = A /m2dv Charge density 電荷密度 Example 24.2. Cell Membrane 細胞膜Ion c

6、hannels are narrow pores that allow ions to pass through cell membranes.離子通道是指容許離子穿越細胞膜的狹窄小孔。A particular channel has a circular cross section 0.15 nm in radius;某通道有一圓形截面，其半徑為 0.15 nm ；it opens for 1 ms and passes 1.1104 singly ionized potassium ions.它張開了 1 ms ，讓 1.1104 個鉀單離子通過。Find both the current

7、 & the current density in the channel.求通道內的電流和電流密度。QIt121.8 10-A12291.8 100.15 10-Am41931.1 101.6 101 10-Cs1.8pAIJA6225 10/A m225/MA m 4 times max. safe current density in household wirings 住宅線路最大安全電流密度的 4 倍Lipid molecules脂分子ion channels離子通道0.3 nmAWG 10 :10 號線22305.7/5.26AJMA mmm24.2. Conduction

8、 Mechanism電導機制E 0 in conductor 導體內 non-electrostatic equilibrium 非靜電平衡 charges accelerated 電荷加速Collisions 碰撞 steady state 穩態JEOhms law, microscopic version歐姆定律歐姆定律，微觀版 conductivity 導電率Ohmic material: independent of E 歐姆材料： 與 E 無關1JE resistivity 電阻率 Vm/A m (m)-1No band gap 無帶溝Large band gap 大帶溝Small

9、band gap 小帶溝Material 材料材料Resistivity電阻率電阻率 (m)Metallic conductors 金屬導體 (20C)Aluminum 鋁2.6510-8Copper 銅1.6810-8Gold 金2.2410-8Iron 鐵9.7110-8Mercury 汞9.8410-7Silver 銀1.5910-8Ionic solutions 離子溶液 ( in water 水中, 18C)1-molar CuSO43.910-41-molar HCl1.710-21-molar NaCl1.410-4H2 O2.6105Blood, human 血，人的0.70S

10、eawater (typical) (海水典型)0.22Semiconductors 半導體 (pure 純, 20C)Germanium 鍺0.47Silicon 硅(舊名矽)23.0Insulators 絕緣體Ceramics 陶瓷1011 - 1014Glass 玻璃1010 - 1014Polystyrene 聚苯乙烯 (保麗龍)1015 - 1017Rubber 橡膠1013 - 1016Wood (dry) 木(乾的)108 - 1014Example 24.3. Household Wiring住宅線路A 1.8-mm-diameter copper wires carries

11、15 A to a household appliance.一條直徑為 1.8-mm 的銅線把 15 A 送到一台家居電器。Find E in the wire.求線中 E 。EJ823151.68 100.90 10Amm-IA99/mVmConduction in Metals金屬內的電傳導Metal 金屬 : 10-8 - 10-6 mAtomic structure: polycrystalline.原子結構：多晶Carriers: sea of “free” electrons, v 106 m/s 載子： ”自由”電子海E = 0: equal # of e moving dire

12、ctions v = 0.往 方向走的 e 數目相等E 0: Collisions between e-ph vd const. e-ph 間的碰撞dvmmveEdt -Steady state:穩態：0dvdtdeEvm -dJne v-2neEmEOhms law歐姆定律 = relaxation time 鬆弛時間TDue to high T Bose statistics of phonons由於聲子的高溫波司统計Cuc.f., vth TIonic Solutions離子溶液Electrolyte: Carriers = e + ions 電解液： 載子 = e + 離子 10-4

13、- 105 mExamples : 例 : Ions through cell membranes.離子穿透細胞膜Electric eels.電鰻。Batteries & fuel cells.電瓶和燃料電池。Electroplating.電鍍。Hydrolysis.水解作用。Corrosion of metal.金屬的銹蝕。Plasmas電漿Plasma: Ionized gas with e & ions as carriers. 電漿：離子化的氣體，載子包括 e 和離子。Examples: 例 : Fluorescent lamps.螢光燈。Plasma displays

14、.電漿顯示器。Neon signs.霓虹燈。Ionosphere.電離層。Flames.火焰。Lightning.閃電。Stars.星球。Rarefied plasma (collisionless) can sustain large I with minimal E.稀薄電漿 (無碰撞) 可以極小 E 維持大 I 。 E.g., solar corona. 例 : 日冕。Semiconductor半導體Pure semiC 純半導體 : T = 0, no mobile charge carriers.無流動電荷載子T 0, thermally excited carriers, e &a

15、mp; holes.熱激發載子 e和洞 increases with T 隨 T 增Doped semiC 摻雜半導體 :Mobile charge carriers from impurities.雜質提供流動電荷載子。N-type: carriers = e. Impurities = Donors. E.g. P in Si. 負-型： 載子 = e。 雜質 = 施子。 例：硅中的磷。P-type: carriers = h. Impurities = Acceptors. E.g. B in Si. 正-型： 載子 = h。 雜質 = 受子。 例：硅中的硼。Thermal motion

16、 dislodges an e .熱運動逐出一粒 e leaving a hole behind.留下一個洞。e & h move oppositely in E 在 E 下， e & h 走的方向相反。Bound e jumps left, h moved to right受困的 e 往左跳， h 就往右移Phosphorous with 5 e有 5 e 的磷P fits into Si lattice, leaving 1 free eP 嵌入Si 晶格中，留下一自由 e 。PN Junction正負接面Current flows in only 1 direction電

17、流祇往一個方向走No battery 無電池無電池 :e & h diffuse across junction & recombine.e & h 朝接面擴散並重組。Junction depleted of carriers.接面缺乏載子。Depletion region乏區Reverse bias 逆向偏壓逆向偏壓 :e & h pulled away from junction.e & h 從接面抽離。Depletion region widens.乏區擴大。I 0.Forward bias 順向偏壓順向偏壓:e & h drawn to

18、junction.e & h 被拉向接面。Depletion region vanishes.乏區消失。I 0.Application: Transistor 應用：三極體（電晶體）Large current change controlled by small signal (at gate):以小訊號 (加於閘極) 控制大電流變化：Amplifier, or擴大器，或Digital switch.數位開關 。Normally channel is closed ( I = 0 ) as one of the junctions is reverse biased.通常通道是關閉的

19、(I = 0 ) ，因為其中一個接面是逆向偏壓。+ V applied to gate attracts e to channel: I 0閘極加上 + V 會吸引 e 到通道： I 0Superconductor超導體Onnes 昂内斯 (1911): Hg = 0 below 低於 4.2K.Muller 繆勒 et al 等 (1986): TC 100K.Current record 目前紀錄 : TC 160K.YBaCuO Applications 應用 :Electromagnets for strong B:強 B 電磁鐵： Labs, MRI, LHC, trains 實驗室

20、，磁振造影儀，大強子碰撞機，高鐵 SQUIDS for measuring weak B.量微弱 B 的SQUIDS 。過渡温度過渡温度電電阻阻率率24.3. Resistance & Ohms Law 電阻和歐姆定律VIROhms Law歐姆定律macroscopic version 巨觀版Open circuit 開路: R I = 0 VShort circuit 短路:R = 0 I VEJIJ AEAVALLRAResistor: piece of conductor made to have specific resistance. 電阻器：有特定電阻值的一塊導體。All

21、heating elements are resistors.所有加熱元件都是電阻器。So are incandescent lightbulbs.白熾燈也是。Table 24.2. Microscopic & Macroscopic Quantities in Ohms Law表24.2.歐姆定律中的微觀和巨觀量MicroscopicMacroscopicRelationVdErIdJALRA1JEVIRE LJ AEJVIR24.4. Electric Power電功率I VElectric Power :電功率：dPqVdtfor time independent V若 V 與時間無關PI V2I R2VRVI RPowe