Transcript Chapter 26
Last time… Equipotential lines Capacitance and capacitors Thur. Oct. 9, 2007 Physics 208 Lecture 12 1 V Q C 1 Parallel plate capacitor V Q /C C o A d -Q Geometrical factor determined from electric fields +Q Energy stored in parallel-plate capacitor 1 1 o A 1 2 2 U CV Ed Ado E 2 2 2 d Energy density Thur. Oct. 9, 2007 2 1 U /Ad o E 2 2 Physics 208 Lecture 12 d 2 Quick Quiz An isolated parallel plate capacitor has charge Q and potential V. The plates are pulled apart. + Which describes the situation afterwards? -Q +Q - pull - d + + pull + A) Charge Q has decreased Cap. isolated Q constant B) Capacitance C has increased C = 0A/d C decreases C) Electric field E has increased E = (Q/A)/0 E constant D) Voltage difference V between plates has increased V= Ed V increases E) None of these Thur. Oct. 9, 2007 Physics 208 Lecture 12 3 Quick Quiz An isolated parallel plate capacitor has a charge q. The plates are then pulled further apart. What happens to the energy stored in the capacitor? -q + + - 1) Increases pull - 2) Decreases d + +q pull + 3) Stays the same Thur. Oct. 9, 2007 Physics 208 Lecture 12 4 Different geometries of capacitors +Q -Q +Q -Q A L d Parallel plate capacitor Q o A C V d Thur. Oct. 9, 2007 Spherical capacitor 1 1 1 Q C 4o a b V Physics 208 Lecture 12 Cylindrical capacitor Q 2o L C V lnb /a 5 Combining Capacitors — Parallel Connect capacitors together with metal wire C1 Ceq C2 “Equivalent” capacitor Potential difference V Both have same V Need different charge Q1 C1 /V Q2 C2 /V Q on each is same Thur. Oct. 9, 2007 Total charge Qeq Q1 Q2 Ceq Qeq V Physics 208 Lecture 12 Q1 Q2 C1 C2 Ceq V 6 Combining Capacitors — Series VA C1 Q Vm Q VA -Q C2 -Q -Q VB VB V VA VB V1 V2 Q Q Q V C1 C1 Ceq V1 VA Vm Q /C1 V2 Vm VB Q/C2 Thur. Oct. 9, 2007 Ceq Q Physics 208 Lecture 12 1 1 1 Ceq C1 C2 7 QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Thur. Oct. 9, 2007 Physics 208 Lecture 12 8 Current in a wire: not electrostatic equilibrium Battery produces E-field in wire Thur. Oct. 9, 2007 Charge moves in response to E-field Physics 208 Lecture 12 9 Electric Current Electric current = I = amount of charge per unit time flowing through a plane perpendicular to charge motion SI unit: ampere 1 A = 1 C / s Depends on sign of charge: + charge particles: current in direction of particle motion is positive - charge particles: current in direction of particle motion is negative Thur. Oct. 9, 2007 Physics 208 Lecture 12 10 Quick Quiz An infinite number of positively charged particles are uniformly distributed throughout an otherwise empty infinite space. A spatially uniform positive electric field is applied. The current due to the charge motion A. increases with time B. decreases with time C. is constant in time D. Depends on field Thur. Oct. 9, 2007 Constant force qE Produces constant accel. qE/m Velocity increases v(t)=qEt/m Charge / time crossing plane increases with time Physics 208 Lecture 12 11 But experiment says… Current constant in time Proportional to voltage 1 I V R Also written J R = resistance (unit Ohm = ) 1 V J = current density = I / (cross-section area) = resistivity = R x (cross-section area) / (length) Thur. Oct. 9, 2007 Resistivity is independent of shape Physics 208 Lecture 12 12 Charge motion with collisions Wire not empty space, has various fixed objects. Charge carriers accelerate, then collide. After collision, charged particle reaccelerates. Result: average “drift” velocity vd Thur. Oct. 9, 2007 Physics 208 Lecture 12 13 Current and drift velocity This average velocity called drift velocity This drift leads to a current e v d E m e 2 I ene Av d ne m Current density J Thur. Oct. 9, 2007 AE Conductivity n e e 2 J I/A E E m Physics 208 Lecture 12 Electric field 14 What about Ohm’s law? Current density proportional to electric field J E Current proportional to current density through geometrical factor Electric field proportional to electric potential through geometrical factor I JA AE Thur. Oct. 9, 2007 A L EL V /R Physics 208 Lecture 12 L L R A A 15 Resistivity Resistivity A R L Independent of sample geometry SI units Ω-m Thur. Oct. 9, 2007 Physics 208 Lecture 12 16 Resistors Circuits Physical layout Schematic layout Thur. Oct. 9, 2007 Physics 208 Lecture 12 17 Quick Quiz Which bulb is brighter? A. A B. B C. Both the same Current through each must be same Conservation of current (Kirchoff’s current law) Charge that goes in must come out Thur. Oct. 9, 2007 Physics 208 Lecture 12 18 I2 Current conservation Iin I1 I3 I1=I2+I3 I1 I3 Iout Iout = Iin Thur. Oct. 9, 2007 I2 I1+I2=I Physics 208 Lecture 12 3 19 Quick Quiz How does brightness of bulb B compare to that of A? A. B brighter than A B. B dimmer than A C. Both the same Battery maintain constant potential difference Extra bulb makes extra resistance -> less current Thur. Oct. 9, 2007 Physics 208 Lecture 12 20