Surface Charge and Resistors

Transcription

1 Surface Charge and Resstors Just after connecton: E may be the same everywhere nav naue thn thck na na thn thck ue ue After steady state s reached: thn thck na thn thck na thn thck ue thn ue thck E thn A A thck thn E thck thn A A thn thck thck

2 Surface Charge Dstrbuton n a Crcut 1. Current must be constant: based on draw dstrbuton of E nav naue 2. Based on E draw approxmate dstrbuton of surface charges

3 A Wde Resstor low moblty nav naue thn thck nau nau thn E thck thn E thck E thn u u thck thn E thck

4 Current at a Node 1 = 2 2 = The current node rule (Krchhoff node or juncton rule [law #1]): In the steady state, the electron current enterng a node n a crcut s equal to the electron current leavng that node

5 Energy n a Crcut V wre = E V battery =? Energy conservaton (the Krchhoff loop rule [2 nd law]): V 1 + V 2 + V 3 + = 0 along any closed path n a crcut V= U/q energy per unt charge

6 Potental Dfference Across the Battery Coulomb force on each e F C non-coulomb force on each e V batt E C E C s FC s e F e NC s 1. a=f/m F 2. F C =ee C E C e 3. F C =F NC Energy nput per unt charge emf electromotve force C The functon of a battery s to produce and mantan a charge separaton. The emf s measured n Volts, but t s not a potental dfference! The emf s the energy nput per unt charge. chemcal, nuclear, gravtatonal

7 Chemcal Battery A battery mantans a potental dfference across the crcut.

8 Chemcal Battery C H 2 H 2 Zn H 2 SO 4 H + H + SO 2-4 H + H + SO 4 2- Zn 2+ ZnSO 4 emf V batt 0.76 V

9 The Frst Chemcal Battery 1780: ug Galvan, boelectrogeness Anmal electrcty 1800: Alessandro Volta: artfcal electrcal organ Alessandro Guseppe Antono Anastaso Volta ( ) 1881: J/C = Volt

10 Internal Resstance of a Battery Drft speed n battery: Maxmum drft speed: E C =0 For large u b : E v b b F NC = F C = ee C V ( emf ) naue nau nau Increase moblty current ncreases Real battery cannot provde current Internal battery resstance lmts maxmum current E F e u E u F / e E net b NC fxed v / F e V emf C NC / C b, max ubfnc e V = 0 C C C /

11 Feld and Current n a Smple Crcut Round-trp potental dfference: V batt V wre 0 emf ( E) 0 E emf I enaue enau emf

12 Feld and Current n a Smple Crcut Round-trp potental dfference: Path 1 V batt V 1 V3 0 emf ( 3 E11 ) ( E3 ) 0 E 1 1 E 2 2 Path 2 V batt V 2 V3 0 emf ( 3 E22 ) ( E3 ) 0

13 V Across Connectng Wres The number or length of the connectng wres has lttle effect on the amount of current n the crcut. V naue nau V wres V flament V battery 0 V nau V battery emf u wres >> u flament V wres V flament V flament (emf ) Work done by a battery goes mostly nto energy dsspaton n the bulb (heat).

14 General Use of the oop Rule V 1 + V 2 + V 3 + V 4 = 0 (V B -V A )+ (V C -V B )+ (V F -V C )+ (V A -V F )=0

15 Applcaton: Energy Conservaton V 1 + V 2 + V 3 + V batt = 0 (-E 1 1 ) + (-E 2 2 ) + (-E 3 3 ) + emf = 0 1. If battery emf=1.5v, what s the voltage drop on thn wre? 2. What s the current n ths crcut?

16 Exercse A Nchrome wre 50 cm long and 0.5 mm thck s connected to a 1.5 V battery. 1. What s the electrc feld nsde the wre? 2. How would t change f we change the wre dameter to 1 mm? 3. What s the current n ths crcut?

17 Twce the ength Nchrome wre (resstve) Quanttatve measurement of current wth a compass V 1 naue nau 2 2 Current s halved when ncreasng the length of the wre by a factor of 2.

18 Two Identcal ght Bulbs n Seres naue nau V Identcal lght bulbs Two dentcal lght bulbs n seres are the same as one lght bulb wth twce as long a flament Electron moblty n metals decreases as temperature ncreases! Conversely, electron moblty n metals ncreases as temperature decreases. Thus, the current n the 2-bulb crcut s slghtly more than that n the one-bulb crcut.

19 Doublng the Cross-Sectonal Area naue nau V oop: emf - E = 0 Electron current n the wre ncreases by a factor of two f the crosssectonal area of the wre doubles. Nchrome wre

20 Two ght Bulbs n Parallel naue V nau 1. Path ABDFA: 2emf E B 0 E B 2 emf 2. Path ACDFA: 2emf E C 0 E C 2 emf 3. Path ABDCA: E B E 0 C length of bulb flament E B E C EB E C F B = C batt = 2 B We can thnk of the two bulbs n parallel as equvalent to ncreasng the cross-sectonal area of one of the bulb flaments.

21 How Do the Currents Know How to Dvde?

22 emf E 0 emf E naue nau Why lght bulb s brghter wth two batteres? emf P 1batt enau emf Two Batteres n Seres Two batteres n seres can drve more current: Potental dfference across two batteres n seres s 2emf doubles electrc feld everywhere n the crcut doubles drft speed doubles current. 2 Work per second: P (q / T )E ee P nauee 2 2emf E 0 E 2emf nau 2emf P 2batt enau 2emf P 2batt 4 P 1batt 2

23 Analyss of Crcuts The current node rule (Charge conservaton) Krchhoff node or juncton rule [1 st law]: In the steady state, the electron current enterng a node n a crcut s equal to the electron current leavng that node Electron current: = naue Conventonal current: I = q naue The loop rule (Energy conservaton) Krchhoff loop rule [2 nd law]: V 1 + V 2 + V 3 + = 0 along any closed path n a crcut V= U/q energy per unt charge