We Are Borg Resistance Is Futile Physics 2102 Jonathan Dowling Physics 2102 Lecture 13 WED 11 FEB Capacitors III Current Resistance Ch25 6 7 Ch26 1 3 Georg Simon Ohm 1789 1854 Exam 01 Sec 2 Dowling Average 67 100 A 90 100 B 80 89 C 60 79 D 50 59 Graders Q1 P1 Dowling NICH 453 MWF 10 30AM 11 30AM Q2 P2 Schafer NICH 222B MW 1 30 2 30 PM Q3 P3 Buth NICH 222A MF 2 30 3 30 PM Q4 P4 Lee NICH 451 WF 2 30 3 30 PM Solutions http www phys lsu edu classes spring2009 phys2102 Go over the solutions NOW Material will reappear on FINAL This problem from our slides first week of class F ii 4 pts What is the direction of the net electrostatic force on the central particle due to the other particles F E F E Units Most common mistake to Compute Magnitude and Direction of Electric Field instead of Electric Force at Central Point This is Sample Problem from Book We worked on Board x F32 F13 q3 x L Charges Alone Could Cancel to Left and To Right Must discuss Big Small Charge versus Small and Big Distance Q vs 1 r2 Common mistake Wrong x k q3 q1 k q3 q2 F31 F32 2 r31 r312 Common mistake To put q3 at L to Left By Symmetry This would only make sense if q3 and q2 were held and q1 was free But we are told q1 and q2 are fixed and q3 is free to move So no symmetry kQ2 4 1 4kQ 2 2 2 2 2 x x x L x L 2 4 x L x 2 2 x L x 2 x L x or 2 x L x x 2L or x 2L 3 Not to right Dielectric Constant If the space between capacitor DIELECTRIC plates is filled by a dielectric the capacitance INCREASES by a factor This is a useful working Q Q C 0 A d definition for dielectric constant Typical values of are 10 200 The and the constant o are both called dielectric constants The has no units dimensionless Atomic View Emol Molecules set up counter E field Emol that somewhat cancels out capacitor field Ecap This avoids sparking dielectric breakdown by keeping field inside dielectric small Ecap Hence the bigger the dielectric constant the more charge you can store on the capacitor Example Capacitor has charge Q voltage V Battery remains connected while dielectric slab is inserted dielectric Do the following increase slab decrease or stay the same Potential difference Capacitance Charge Electric field Example Initial values capacitance C charge Q potential difference V electric field E Battery remains connected V is FIXED Vnew V same dielectric slab Cnew C increases Qnew C V Q increases Since Vnew V Enew V d E same Energy stored u 0E2 2 u 0E2 2 E2 2 Summary Any two charged conductors form a capacitor Capacitance C Q V Simple Capacitors Parallel plates C 0 A d Spherical C 4 0 ab b a Cylindrical C 2 0 L ln b a Capacitors in series same charge not necessarily equal potential equivalent capacitance 1 Ceq 1 C1 1 C2 Capacitors in parallel same potential not necessarily same charge equivalent capacitance Ceq C1 C2 Energy in a capacitor U Q2 2C CV2 2 energy density u 0E2 2 Capacitor with a dielectric capacitance increases C kC What are we going to learn A road map Electric charge Electric force on other electric charges Electric field and electric potential Moving electric charges current Electronic circuit components batteries resistors capacitors Electric currents Magnetic field Magnetic force on moving charges Time varying magnetic field Electric Field More circuit components inductors Electromagnetic waves light waves Geometrical Optics light rays Physical optics light waves Resistance is NOT Futile Electrons are not completely free to move in a conductor They move erratically colliding with the nuclei all the time this is what we call resistance The resistance is related to the potential we need to apply to a device to drive a given current through it The larger the resistance the larger the potential we need to drive the same current Ohm s laws V R i Units R V and therefore i R and V iR Volt Ohm abbr Ampere Georg Simon Ohm 1789 1854 a professor who preaches such heresies is unworthy to teach science Prussian minister of education 1830 Devices specifically designed to have a constant value of R are called resistors and symbolized by dq C Ampere A i s dt Current density and drift speed Vector Same direction as E J such that i J dA The current is the flux of the current density If surface is perpendicular to a constant electric field then i JA or J i A Units J J Ampere m2 dA E i Drift speed vd Velocity at which electrons move in order to establish a current Charge q in the length L of conductor q n A L e L n density of electrons e electric charge A E t i L vd i q n ALe n A e vd L t vd i J n Ae n e J n e vd vd Resistivity and resistance Metal field lines These two devices could have the same resistance R when measured on the outgoing metal leads However it is obvious that inside of them different things go on resistivity E or as vectors E J J Resistivity is associated resistance R V I m Ohm meter with a material resistance with respect to a device 1 Conductivity constructed with the material Example A L V V E L i J A Makes sense For a given material V L RA i L A L R A Longer More resistance Thicker Less resistance Resistivity and Temperature Resistivity depends on temperature 0 1 T T0 At what temperature would the resistance of a copper conductor be double its resistance at 20 0 C Does this same doubling temperature hold for all copper conductors regardless of shape or size b a Power in electrical circuits A battery pumps charges through the resistor or any device by producing a potential difference V between points a and b How much work does the battery do to move a small amount of charge dq from b to a dW dU dq V dq dt dt V iV dt The battery power is the work it does per unit time P dW dt iV P iV is true for the battery pumping charges through any device If the device follows Ohm s law i e it is a resistor then V iR and P iV i2R V2 R
View Full Document
Unlocking...