Physics 2102 Lecture 13: WED 11 FEB Jonathan Dowling We Are Borg. Resistance Is Futile! Physics 2102 Lecture 13: WED 11 FEB Capacitors III / Current & Resistance Ch25.6–7 Ch26.1–3 Georg Simon Ohm (1789-1854)

Sec. 2 (Dowling) Average: 67/100 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≠E! Units! Most common mistake to Compute Magnitude and Direction of Electric Field instead of Electric Force at Central Point. (ii) (4 pts) What is the direction of the net electrostatic force on the central particle due to the other particles? F≠E!

Common mistake: Wrong x. This is Sample Problem from Book We worked on Board x q3 Charges Alone Could Cancel to Left and To Right. Must discuss Big & Small Charge versus Small and Big Distance: Q vs. 1/r2 x–L F32 F13 Common mistake: Wrong x. 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! Not to right.

Dielectric Constant C =  A/d If the space between capacitor plates is filled by a dielectric, the capacitance INCREASES by a factor  This is a useful, working definition for dielectric constant. Typical values of are 10–200 +Q –Q DIELECTRIC C =  A/d 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. Hence the bigger the dielectric constant the more charge you can store on the capacitor. Ecap

Example Capacitor has charge Q, voltage V Battery remains connected while dielectric slab is inserted. Do the following increase, decrease or stay the same: Potential difference? Capacitance? Charge? Electric field? dielectric slab

Example Initial values: capacitance = C; charge = Q; potential difference = V; electric field = E; Battery remains connected V is FIXED; Vnew = V (same) Cnew = kC (increases) Qnew = (kC)V = kQ (increases). Since Vnew = V, Enew = V/d=E (same) dielectric slab Energy stored? u=e0E2/2 => u=ke0E2/2 = eE2/2

Summary Any two charged conductors form a capacitor. Capacitance : C= Q/V Simple Capacitors: Parallel plates: C = e0 A/d Spherical : C = 4 e0 ab/(b-a) Cylindrical: C = 2 e0 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 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

Current density and drift speed The current is the flux of the current density! E i J dA If surface is perpendicular to a constant electric field, then i=JA, or J=i/A Units: Drift speed: vd :Velocity at which electrons move in order to establish a current. E i L A Charge q in the length L of conductor: n =density of electrons, e =electric charge

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: Resistivity is associated with a material, resistance with respect to a device constructed with the material. ( resistance: R=V/I ) Example: A L V + - Makes sense! For a given material:

Resistivity and Temperature Resistivity depends on temperature: r = r0(1+a (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?

Power in electrical circuits b a 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