Chapter 27CurrentResistance AndResistorElectric Current, the definitionAssume charges are moving perpendicular to a surface of area AIf ΔQ is the amount of charge that passes through A in time Δt, then the average current istQIavg∆∆=ordtdQI =+++ +++IAAnyone notices a difference of this figure compared with the one in the book?If yes, and explain why I draw it this way. Correct answer = 1 bonus pointHow many of you preview, review, do homework within 2 days of class, 2 days toward due date?Electric Current, definition and unitElectric current is the rate of flow of charge through some region of spaceThe SI unit of current is the ampere (A)1 A = 1 C / sAnd ampere is a base unit. The unit for time, second, is also a base unit. The unit for charge is then defined as 1C=1A/1sThe symbol for electric current is IDirection of CurrentThe charges passing through the area could be positive or negative or both. This area may or may not be an actual physical surface and the charges can flow in a conductor or in vacuum.It is conventional to assign to the current the same direction as the flow of positive chargesThe direction of current flow is opposite the direction of the flow of electronsIt is common to refer to any moving charge as a charge carrierCurrent in a conductor and the drift speedCharged particles move through a conductor under the drive of an electric field inside.Wait! There should be no electric field inside a conductor. Explanation please!EAssume a cross-sectional area A that is perpendicular to and the number of charge carriers per unit volume n.Then nAΔx is the total number of charge carriersdVCurrent linearly proportional to drift speedThe total charge is the number of carriers times the charge per carrier, qΔQ = (nAΔx)qThe drift speed, vd, is the speed at which the carriers movevd= Δx / Δt and∆x = vd∆tRewritten: ΔQ = (nAvdΔt)qFinally, current, Iave= ΔQ/Δt = nqvdAThis is to say that current is linearly proportional to the drift speed vdA typical value of the drift speedAssume a copper wire, with one free electron per atom contributed to the currentThe drift speed for a 12-gauge copper wire carrying a current of 10.0 A is 2.23 x 10-4m/sThis is a typical order of magnitude for drift speedsThis is very slow, how come when a switch is closed, the light comes on from a light bulb ~ 10m away? It should take ~10/ 2.23 x 10-4sec which is about 12 hours.What is wrong?Motion of the charge carrier, the electrons, in a conductorThe actual charge carrier in conductor is the electronThe zigzag black lines represents the motion of a charge carrier in a conductorThe net drift speed is smallThe sharp changes in direction are due to collisionsThe net motion of electrons is opposite the direction of the electric fieldThe current direction is conventionally defined to be the positive carrier motion direction, or the electric field direction.PLAYACTIVE FIGUREMotion of Charge Carriers, final discussionThe electric field exerts forces on the electrons in the wire at the same time (almost). These forces cause the electrons to move in the wire and create a current. So the current starts to flow anywhere in the circuit when the switch is closed. In the presence of an electric field, like the one set up by a battery, in spite of all the collisions, the charge carriers slowly move along the conductor with a drift velocity,The battery does not supply the electrons, it only establishes the electric fielddvCurrent Density J, the definitionCurrent density is a vector and is in the direction of the positive charge carriersdnqV=JJJJThe current density J of the current I in a conductor is defined as the current per unit areaJ has SI units of A/m2∫⋅= AdI JJJJThe relationship to the current isConductivity, the definitionA current density and an electric field are established in a conductor whenever a potential difference is maintained across the conductorFor some materials, the current density is directly proportional to the field, that is The constant of proportionality, σ, is called the conductivityof the
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