A Little Capacitance and Current and ResistanceNotesDIELECTRIC RESULTSAPPLICATION OF GAUSS’ LAWNew Gauss for DielectricsNew Topic: Current and ResistancePhysical ResistorsWhat Happens?What’s Moving?What is making the charged move??KEEP IN MINDDEFINITIONSlide 13UNITSSlide 15Comment on Current FlowQuestion …..Slide 18ANOTHER DEFINITIONSlide 20OhmOhm’s LawGraphA DIODELet’s look at the atomic level ..Slide 26Slide 27The CurrentNotationSlide 30We return to the diagram …..Starting when the electron is at rest:FinallyReferencePonderSlide 36ConductivitySlide 38Slide 39Slide 40Going to the usual limit …ExampleRange of r and sYe old RESISTANCEREMEMBERTemperature EffectA closed circuitPowerA Little CapacitanceA Little CapacitanceandandCurrent and ResistanceCurrent and ResistanceFebruary 19, 2006February 19, 2006Notes Notes Complete Capacitance (Very Brief)Complete Capacitance (Very Brief)New topic today – Current and New topic today – Current and ResistanceResistanceQuiz on FridayQuiz on FridayFriday 7:30 review session.Friday 7:30 review session.There is a new WebAssign.There is a new WebAssign.DIELECTRIC RESULTS000EECCVVAPPLICATION OF GAUSS’ LAWqqqandAqEEAqqEAqE''00000New Gauss for Dielectrics00-sometimesqdfreeAENew Topic:Current and ResistancePhysical ResistorsWhat Happens?“+”“+”“+”“+”REMEMBER, THE ELECTRONSARE ACTUALLY MOVING THEOTHER WAY!--What’s Moving?What is making the charged move??BatteryKEEP IN MINDA wire is a conductorWe will assume that the conductor is essentially an equi-potentialIt really isn’t.Electrons are moving in a conductor if a current is flowing. This means that there must be an electric field in the conductor.This implies a difference in potential since E=V/dWe assume that the difference in potential is small and that it can often be neglected.In this chapter, we will consider this difference and what causes it.DEFINITIONCurrent is the motion of POSITIVE CHARGE through a circuit. Physically, it is electrons that move but …Conducting materialQ,tConducting materialQ,tdtdqiortQiCURRENTUNITSA current of one coulomb per second is defined as ONE AMPERE.A charged belt, 30 cm wide, travels at 40 m/s between a source of charge and a sphere. The belt carries charge into the sphere at a rate corresponding to 100 µA. Compute the surface charge density on the belt.[8.33e-06] C/m2Comment on Current FlowA small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is ω. What average current does this rotating charge represent? Question …..An electric current is given by the expression I(t) = 100 sin(120πt), where I is in amperes and t is in seconds. What is the total charge carried by the current from t = 0 to t = (1/240) s?ANOTHER DEFINITIONAIareacurrentJ The figure represents a section of a circular conductor of non-uniform diameter carrying a current of 5.00 A. The radius of cross section A1 is 0.400 cm. (a) What is the magnitude of the current density across A1? (b) If the current density across A2 is one-fourth the value across A1, what is the radius of the conductor at A2?OhmA particular object will resist the flow of current.It is found that for any conducting object, the current is proportional to the applied voltage.STATEMENT: V=IRR is called the resistance of the object.An object that allows a current flow of one ampere when one volt is applied to it has a resistance of one OHM.Ohm’s LawIRV GraphIRV A DIODEResistance Varies with Applied Voltage (actually with current)Let’s look at the atomic level ..Conduction is via electrons.They are weak and small and don’t exercise much.Positive charge is big and strong and doesn’t intimidate easily.It’s an ugly situation … something like ……-+lVVabEThe CurrentElectrons are going the opposite way from the current. (WHY?)They probably follow a path like …Average “drift”speed - vdOUTINNotationvdaverage drift velocity of the electronn number of electrons (mobile) per unit volume.t interval of timex average distance the electron moves in time t.Q total amount of CHARGE that goes through a surface of the conductor in time  t.dvJ nenevAIJenAvtQIetnAvQdavgdavgd )(Often a VectorThe DiagramWe return to the diagram …..Consider an electron.Assume that whenever it “bumps” into something it loses its momentum and comes to rest.It’s velocity therefore starts at zero, the electric field accelerates it until it has another debilitating collision with something else.During the time it accelerates, its velocity increases linearly .The average distance that the electron travels between collisions is called the “mean free path”.Starting when the electron is at rest:meEvvmeEmFaatatvvd0Let n= number of charge carriersper unit volume (mobile electrons)We showed two slides ago::122mnesoEmEneJormeEnenevnqvJddFinallydvReference The average drift velocity of an electron is about 10-4 m/sPonderHow can a current go through a resistor and generate heat (Power) without decreasing the current itself?Loses EnergyGets it backExitConductivityIn metals, the bigger the electric field at a point, the bigger the current density.EJ is the conductivity of the material.=(1/) is the resistivity of the material )(100TT A conductor of uniform radius 1.20 cm carries a current of 3.00 A produced by an electric field of 120 V/m. What is the resistivity of the material?The rod in the figure is made of two materials. The figure is not drawn to scale. Each conductor has a square cross section 3.00 mm on a side. The first material has a resistivity of 4.00 × 10–3 Ω · m and is 25.0 cm long, while the second material has a resistivity of 6.00 × 10–3 Ω · m and is 40.0 cm long. What is the resistance between the ends of the rod?Going to the usual limit …JdAIanddAdIJExampleA cylindrical conductor of radius R has a current density given by(a) J0 (constant)(b) rFind the total current in each