Slide 1Electrical currentSlide 3Slide 4Slide 5Slide 6Slide 7Resistivity and TemperaturePower in electrical circuitsEmf devices and single loop circuitsCircuit problemsSummaryExampleExampleExampleExampleIncandescent light bulbsExamplePhysics 2102 Current and resistancePhysics 2102Gabriela GonzálezGeorg Simon Ohm (1789-1854)In a conductor, electrons are free to move. If there is a field E inside the conductor, F=qE means the electrons move in a direction opposite to the field: this is an electrical current.EWe think of current as motion of imaginary positive charges alongthe field directions. dtiqdtdqi ,AmperesecondCoulomb[i] :UnitsAndre-MarieAmpere1775-1836Electrical currentWasn’t the field supposed to be zero inside conductors?Yes, if the charges were in equilibrium. The reasoning was “electrons move until they cancel out the field”. If the situation is not static, that is, if electrons are moving, then the field can be nonzero in a conductor, and the potential is not constant across it!However, “somebody” has to be pumping the electrons: this is the job of the battery we put across a circuit. If there is no source creating the electric field, the charges reach equilibrium at E=0.Electrical currentECurrent is a scalar, NOT a vector, although we use arrows to indicate direction of propagation. Current is conserved, because charge is conserved!1i2i3i321iii Electrical current:Conservation“junction rule”: everything that comes in, must go out.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. ) (abbr. OhmAmpereVolt [R] :Units Georg Simon Ohm (1789-1854)"a professor who preaches such heresies is unworthy to teach science.” Prussian minister of education 1830iVR iRVRVi and : thereforeandOhm’s lawsDevices specifically designed to have a constant value of R are calledresistors, and symbolized byElectrons 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”.ResistanceJ :VectorE as direction Same AdJi that suchEiJdAIf surface is perpendicular to a constant electric field, then i=JA, or J=i/ADrift speed: vd :Velocity at which electrons move in order to establish a current.EiLACharge q in the length L of conductor:eLAnq )(n =density of electrons, e =electric chargedvLt ddveAnvLeLAntqi enJeAnivddvenJCurrent density and drift speedThe current is the flux of the current density!2mAmpere][ JUnits:Where is the (current, current density, electron density, drift velocity, electric field) largest?These two devices could have the same resistanceR, when measured on the outgoing metal leads.However, it is obvious that inside of them different things go on.Metal“field lines”resistivity:JEJE vectors,as or, Resistivity is associatedwith a material, resistancewith respect to a deviceconstructed with the material.1 :tyConductivi Example:ALV+-AiJLVE ,LARAiLVALRMakes sense!For a given material: resistance LessThickerresistance MoreLonger Resistivity and resistance( resistance: R=V/I )Resistivity and Temperature• 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? Resistivity depends on temperature: r = r0(1+a (T-T0) )baPower in electrical circuitsA 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 dtThe battery “power” is the work it does per unit time: P=dW/dt=iVP=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/RbaThe battery operates as a “pump” that movespositive charges from lower to higher electric potential. A battery is an example of an “electromotive force” (EMF) device. These come in various kinds, and all transform one source of energy into electrical energy. A battery uses chemical energy, a generator mechanical energy, a solar cell energy from light, etc.The difference in potential energy that thedevice establishes is called the EMFand denoted by E.Emf devices and single loop circuitsVa+ E -iR=VaE = iRa b c d=aVaiRbadc- +iiEGiven the emf devices and resistors in a circuit, we want to calculate the circulating currents. Circuit solving consists in “taking a walk” along the wires. As one “walks” through the circuit (in any direction) one needs to follow two rules:When walking through an EMF, add +E if you flow with the current or - Eotherwise. How to remember: current “gains” potential in a battery.When walking through a resistor, add -iR, if flowing with the current or +iRotherwise. How to remember: resistors are passive, current flows “potential down”.Example:Walking clockwise from a: + E-iR=0.Walking counter-clockwise from a: - E+iR=0.baCircuit problemsSummary•Current and current density: i=dq/dt; i=∫ J · dA ; J=nevd•Resistance and resistivity: V= iR ; E=Jr; R=r L/A; r=r0(1+a(T-T0))•Power: P=iV= (V2/R =i2R)•Walking a circuit: E-iR =0ExampleA human being can be electrocuted if a current as small as 50 mA passes near the heart. An electrician working with sweaty hands makes good contact with the two conductors he is holding. If his resistance is 1500 W , what might the fatal voltage be?(Ans: 75 V)ExampleTwo conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1.0 mm. Conductor B is a hollow tube of outside diameter 2.0 mm and inside diameter 1.0 mm. What is the resistance ratio RA/RB, measured between their ends?BAAA=p r2AB=p ((2r)2-r2)=3pr2R=rL/ARA/RB= AB/AA= 3ExampleA 1250 W radiant heater is constructed to operate at 115 V. (a) What will be the current in the heater? (b) What is the resistance of the heating coil? (c) How much thermal energy is produced in 1.0 h by the heater?• Formulas: P=i2R=V2/R; V=iR • Know P, V; need R to calculate
View Full Document
Unlocking...