Parallel plate capacitor. Last time. Parallel plate capacitor. What is the potential difference? What is the capacitance? Quick Quiz "V = 1 C Q

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1 Last time r r r V=V o Potentia an eectric fie Capacitors "V = 1 C Q Parae pate capacitor Charge Q move from right conuctor to eft conuctor Each pate has size Length With = Area = A outer Pate surfaces behave as sheets of charge, each proucing Efie Q Q inner Friay Honors Lecture: Prof.. Moss, Physioogy Detecting the boy s eectrica signas Tues. Oct. 11, 2007 Physics 208 Lecture 12 1 Tues. Oct. 11, 2007 Physics 208 Lecture 12 2 Parae pate capacitor Charge ony on inner surfaces of pates. Efie insie superposition of Efie from each pate. Constant Efie insie capacitor. σ σ What is the potentia ifference? Eectric fie between pates E eft E right = " /2# o " /2# o = " /# o Uniform eectric fie Potentia ifference = V V = (1/q)( work to move charge from to minus pate) ( ) " (#(#qe)) = 1/q ' $V = E = % /& o = Q * ), (& o A Q E tota Q Tues. Oct. 11, 2007 Physics 208 Lecture 12 3 Tues. Oct. 11, 2007 Physics 208 Lecture 12 4 What is the capacitance? % "V = V #V # = Q ( ' * & $ o A) "V = Q/C C = " o A This is a geometrica factor Q Tues. Oct. 11, 2007 Physics 208 Lecture 12 5 Q An isoate parae pate capacitor with spacing has charge q. The pates are e a sma istance further apart. Which of the foowing escribe situation after motion? A) The charge ecreases B) The capacitance increases C) The eectric fie increases D) The votage between the pates increases E) None of these q Tues. Oct. 11, 2007 Physics 208 Lecture 12 6 q C = ε 0 A/ C ecreases! E= q/(ε 0 A) E constant V= E V increases 1

2 Work one to charge a capacitor equires work to transfer charge q from one pate: W = "Vq = q C q Energy store in a capacitor Energy store = work one U = Q2 2C = 1 2 Q"V = 1 2 C ("V )2 Eampe: parae pate capacitor Tota work require = sum of incrementa work: U = 1 2 ( A)" E 2 o W = Q q " q = Q2 0 C 2C Energy ensity U / A ( ) = 1 2 " oe 2 epens ony on fie strength Tues. Oct. 11, 2007 Physics 208 Lecture 12 7 Tues. Oct. 11, 2007 Physics 208 Lecture 12 8 An isoate parae pate capacitor has a charge q. The pates are then e further apart. What happens to the energy store in the capacitor? 1) Increases 2) Decreases q q 100 µm Human capacitors Ce membrane: Empty space separating charge fuis (conuctors) ~ 7 8 nm thick In combination w/fuis, acts as paraepate capacitor Etraceuar fui 3) Stays the same Tues. Oct. 11, 2007 Physics 208 Lecture 12 9 Tues. Oct. 11, 2007 Physics 208 Lecture Moeing a ce membrane Ce membrane epoarization 78 nm K A Etraceuar fui Na C Ionic charge at surfaces of conucting fuis Capacitance: " o A ΔV~0.1 V ( 8.85 #10 $12 F /m)4% 50 #10 $6 m = 8 #10 $9 m Charges are / ions instea of eectrons Charge motion is through ce membrane (ion channes) rather than through wire Otherwise, acts as a capacitor ~0.1 V resting potentia 100 µm sphere surface area ( ) 2 ~ cm 2 = 3.5 #10 $11 F = 35pF 78 nm K A Etraceuar fui Na C ΔV~0.02 ΔV~0.1 V V Ce membrane can reverse potentia by opening ion channes. Potentia change ~ 0.12 V Ions fow through ion channes Channe spacing ~ 10 membrane thickness (~ 100 channes / µm 2 ) Charge fer require ΔQ=CΔV=(35 pf)(0.12v) =( C/V)(0.12V) = Couombs C/ion > ions fow This is an eectric current! ~0.1µF/cm 2 Tues. Oct. 11, 2007 Physics 208 Lecture Tues. Oct. 11, 2007 Physics 208 Lecture

3 Charge motion Ce membrane capacitor: ~70 ions fow through each ion channe to epoarize membrane Occurs in ~ 1 ms = sec. This is a current, units of Couombs / sec 1 Couomb / sec = 1 Amp Eectric Current Eectric current = I = amount of charge per unit time fowing through a pane perpenicuar to charge motion SI unit: ampere 1 A = 1 C / s Depens on sign of charge: charge partices: current in irection of partice motion is positive charge partices: current in irection of partice motion is negative Tues. Oct. 11, 2007 Physics 208 Lecture Tues. Oct. 11, 2007 Physics 208 Lecture Current in a wire An infinite number of positivey charge partices are uniformy istribute throughout an otherwise empty infinite space. A spatiay uniform positive eectric fie is appie. The current ue to the charge motion Battery prouces Efie in wire A. increases with time B. ecreases with time C. is constant in time D. Depens on fie Constant force qe Prouces constant acce. qe/m Veocity increases v(t)=qet/m Charge / time crossing pane increases with time Current fows in response to Efie Tues. Oct. 11, 2007 Physics 208 Lecture Tues. Oct. 11, 2007 Physics 208 Lecture But eperiment says Current constant in time Proportiona to votage = resistance (unit Ohm = Ω) I = 1 V Aso written J = current ensity = I / (crosssection area) ρ = resistivity = (crosssection area) / (ength) J = 1 " V esistivity is inepenent of shape Tues. Oct. 11, 2007 Physics 208 Lecture Charge motion with coisions Suppose space not empty, but has various fie objects. The charge partices wou then coie with these objects. Assumption: after coision, charge partice equay ikey to move in any irection. Before coision Tues. Oct. 11, 2007 Physics 208 Lecture After coision 3

4 Two cyinrica conuctors are mae from the same materia. They are of equa ength but one has twice the iameter of the other. 1 2 A. 1 < 2 B. 1 = 2 esistors Circuits Physica ayout C. 1 > 2 Current fow ~ uniform. More crosssectiona area means more current fowing ess resistance. = " A L Schematic ayout Tues. Oct. 11, 2007 Physics 208 Lecture Tues. Oct. 11, 2007 Physics 208 Lecture Which bub is brighter? A. A B. B C. Both the same Current conservation I in I 1 I 1 I 1 =I 2 I 3 I 2 I 3 I 3 Current through each must be same Conservation of current (Kirchoff s current aw) Charge that goes in must come out Tues. Oct. 11, 2007 Physics 208 Lecture I out = I in I out I 2 I 1 I 2 =I 3 Tues. Oct. 11, 2007 Physics 208 Lecture How oes brightness of bub B compare to that of A? A. B brighter than A B. B immer than A C. Both the same Battery maintain constant potentia ifference Etra bub makes etra resistance > ess current Tues. Oct. 11, 2007 Physics 208 Lecture esistors in Series I 1 = I 2 = I Potentias a ΔV = ΔV 1 ΔV 2 = I 1 I 2 = = I ( 1 2 ) The equivaent resistance eq = 1 2 = 2 2 resistors in series: L Like summing engths = " L A Tues. Oct. 11, 2007 Physics 208 Lecture

5 What happens to the brightness of the bub B when the switch is cose? A. Gets immer B. Gets brighter C. Stays same D. Something ese Battery is constant votage, not constant current What happens to the brightness of the bub A when the switch is cose? A. Gets immer B. Gets brighter C. Stays same D. Something ese Tues. Oct. 11, 2007 Physics 208 Lecture Tues. Oct. 11, 2007 Physics 208 Lecture esistors in Parae ΔV = ΔV 1 = ΔV 2 I = I 1 I 2 (ower resistance path has higher current) Equivaent esistance /2 A areas = " L A Tues. Oct. 11, 2007 Physics 208 Lecture