Chapter 27ReviewReviewCurrent Density J, the definitionConductivity and Ohm’s LawOhm’s LawResistance and a more popular form of Ohm’s LawResistance, discussionResistivity Values and the temperature coefficient αResistance and ResistorsOhmic Material, GraphNonohmic Material, GraphResistance and TemperatureResistivity and Temperature, Graphical ViewElectrical Power: work down by the electric field in the circuitElectric Power, to summarizeExample: Electric Power TransmissionExample: two incandescent light bulbsSlide 19Chapter 27CurrentResistance And ResistorReviewThe current is defined and its unit is ampere (A), a base unit in the SI system.dtdQI +++ +++IAThe charges passing through the area could be positive or negative or both. They are called charge carriers. Current direction is chosen to the electric field direction or the direction as the flow of positive charges.The motion of the charge carriers is the result of the movement driven by the electric field plus random collisions with other particles in the conductor. The average velocity of this motion is called the drift velocity Reviewn is the number of charge carriers per unit volume.q is the carrier chargeThe drift velocity is very small. What is actually prorogating in the conducting wire is the electric field. So the conducting wire is actually the carrier or guide for the electric field, which delivers the electric power.EdVThe current and the drift velocity has a linear relationship.dI nq= �rrv ACurrent Density J, the definitionCurrent density is a vector and is in the direction of the positive charge carriers, or in the direction of the electric field.dnqVJThe current density J of the current I a conductor is defined as the current per unit areaJ has SI units of A/m2 AdI JCompare with, one has: dI nq= �rrv AConductivity and Ohm’s LawFor some materials, the current density is directly proportional to the electric field:EJThe constant of proportionality, σ, is called the conductivity of the conductor. Another often used parameter is resistivity, ρis just inverse of the conductivity: ρ σAnd this formula, is called Ohm’s Law.EJOhm’s LawOhm’s law states the ratio of the current density to the electric field is a constant σMathematically, J = σ EMost metals obey Ohm’s lawMaterials that obey Ohm’s law are said to be ohmicNot all materials follow Ohm’s lawMaterials that do not obey Ohm’s law are said to be nonohmicOhm’s law is not a fundamental law of natureOhm’s law is an empirical relationship valid only for certain materialsButResistance and a more popular form of Ohm’s LawFrom Ohm’s Law:lrEJ Es=One has:1E J Jrs= =Now exam the section of wire with length and cross section A, one has:l1 I lV El Jl Jl l IA AD r r rs= = = = =Now we define a new parameter, the resistance of this section of the wire, R:lRAr�VRID�Ohm’s Law becomesorV RID =Resistance, discussionSI units of resistance are ohms (Ω)1 Ω = 1 V / ASI units of resistivity are Ω·m Resistance proportional to the resistivity constant of the material, the length of the conductor (wire), inversely proportional to the cross section. In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductorThe constant of proportionality is called the resistance of the conductorlRAr�VRID�V RID =Resistivity Values and the temperature coefficient αResistance and ResistorsAll (almost) materials have resistanceThose that are call ohmic if Ohm’s Law holds.VRID�In a circuit, the resistance of connecting wires (PCB copper traces) are often neglected. A device made to have certain resistance value is call a resistor.Ohmic Material, GraphFor an ohmic deviceThe resistance is constant over a wide range of voltagesThe relationship between current and voltage is linearThe slope is related to the resistanceNonohmic Material, GraphNonohmic materials are those whose resistance changes with voltage or currentThe current-voltage relationship is nonlinearA junction diode is a common example of a nonohmic deviceResistance and TemperatureOver a limited temperature range, the resistivity of a conductor varies approximately linearly with the temperatureρo is the resistivity at some reference temperature To To is usually taken to be 20oCα is the temperature coefficient of resistivitySI units of α are oC-1With a resistor:This is often used to measure temperature with materials that have large α[1 ( )]o oρ ρ α T T= + -= + -[1 ( )]o oR Rα T TResistivity and Temperature, Graphical ViewFor some metals, the resistivity is nearly proportional to the temperatureA nonlinear region always exists at very low temperaturesThe resistivity usually reaches some finite value as the temperature approaches absolute zeroElectrical Power: work down by the electric field in the circuitAs a charge Q moves from a to b, the electric potential energy of the system increases by QVThis energy comes from the chemical energy in the batteryAs the charge moves through the resistor (c to d), the system loses this electric potential energy, turning it to heat by the resistorThe electric power (energy time rate) the resistor consumes is PLAYACTIVE FIGUREQQD= = = �Denergy Q Vp I Vtime t�dQIdtbecauseso= �Dp I VWith Ohm’s Law:D= =22Vp I RRElectric Power, to summarizeThe electric power is given by the equation:and is always correct.If Ohm’s Law is applicable, alternative expressions are often useful:Units: I is in A, R is in Ω, V is in V, and is in WI= D p V( )I ID= D = =22 Vp V RRpExample: Electric Power TransmissionThe question:Dallas needs 100 MW electric power which is generated 100 miles away. The transmission line (aluminum) has a diameter of 2 inches. How much power must be generated to deliver 100 MW to Dallas, (a) If 110 V is used? (b) if 600,000 V is used?Example: two incandescent light bulbs In the US, the standard in our grid power system is 110 V. When two incandescent light bulbs (a pure resistive device, with light output proportional to the power consumed), with power specifications of 60 W and 100 W, are connected in parallel, which one is brighter?Example: two incandescent light bulbs Now connect them in series, which one is brighter in this
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