Direc Curren Physics for Scieniss & Engineers 2 Spring Semeser 2005 Lecure 16 This week we will sudy charges in moion Elecric charge moving from one region o anoher is called elecric curren Curren is all around us Curren is flowing hrough ligh bulbs, ipods, and lighning srikes Curren consiss of mobile elecrons raveling in conducing maerials Direc curren is defined as a curren ha flows in one direcion. February 3, 2005 Physics for Scieniss&Engineers 2 1 February 3, 2005 Physics for Scieniss&Engineers 2 2 Elecric Curren We define he elecric curren i as he ne charge passing a given poin in a given ime Random moion of elecrons in conducors or he flowing of elecrically neural aoms are no curren in spie of he fac ha large amouns of charge are moving pas a given poin If ne charge dq passes a poin in ime d we define he curren i o be i = dq d February 3, 2005 Physics for Scieniss&Engineers 2 3 Elecric Curren (2) The amoun of charge q passing a given poin in ime is he inegral of he curren wih respec o ime given by q = dq = id 0 We will use charge conservaion, implying ha charge flowing in a conducor is never los Therefore he same amoun of charge mus flow hrough one end of he conducor ha exis from he oher end of he conducor. February 3, 2005 Physics for Scieniss&Engineers 2 4 1
The Ampere The uni of curren is coulombs per second, which has been given he uni ampere, named afer French physicis André Ampère, (1775-1836) The ampere is abbreviaed as A and is given by Some ypical currens are Flashligh - 1 A The sarer in your car - 200 A ipod - 50 ma 1 A = 1 C 1 s In a lighning srike (for a shor ime) - 100,000 A Baeries In he following days we will make exensive use of baeries as devices ha provide direc currens in circuis If you examine a baery, you will find is volage wrien on i This volage is he poenial difference i can provide o a circui You will also find heir raings in unis of mah This raing provides informaion on he oal charge ha hey can deliver when fully charged The quaniy mah is anoher uni of charge: 1 mah = (10 3 A)(3600 s) = 3.6 As = 3.6 C February 3, 2005 Physics for Scieniss&Engineers 2 5 February 3, 2005 Physics for Scieniss&Engineers 2 6 Curren is a scalar Curren Curren has a sign bu no a direcion This week we will represen he direcion of he curren flowing in a conducor using an arrow This arrow represens wheher he ne curren is posiive or negaive in a conducor a a given poin bu does no represen a direcion in hree dimensions Physically he charge carriers in a conducor are elecrons ha are negaively charged However, as is convenionally done, we define posiive curren as he ne flow of posiive charge carriers pas a given poin per uni ime. Curren Densiy Le s consider curren flowing in a conducor Taking a plane hrough he conducor, we can define he curren per uni area flowing hrough he conducor a ha poin as he curren densiy J We ake he direcion of J as he direcion of he velociy of he charges crossing he plane If he cross secional area is small, he magniude of J will be large If he cross secion area is large, he magniude of J will be small. February 3, 2005 Physics for Scieniss&Engineers 2 7 February 3, 2005 Physics for Scieniss&Engineers 2 8 2
Curren Densiy (2) The curren flowing hrough he surface is i = J d A where is he differenial area elemen perpendicular o he surface. If he curren is consan and perpendicular o he surface, hen and we can wrie an expression for he magniude of he curren densiy J = i A Elecron Drif Velociy In a conducor ha is no carrying curren, he conducion elecrons move randomly When curren flows hrough he conducor, he elecrons sill move randomly bu wih an added drif velociy, v d The magniude of he velociy of random moion is on he order of 10 6 m/s while he magniude of he drif velociy is on he order of 10-4 m/s We can relae he curren densiy J o he drif velociy v d of he moving elecrons February 3, 2005 Physics for Scieniss&Engineers 2 9 February 3, 2005 Physics for Scieniss&Engineers 2 10 Elecron Drif Velociy (2) Consider a conducor wih cross secional area A and elecric field E Suppose ha here are n elecrons per uni volume. The negaively charged elecrons will drif in a direcion opposie o he elecric field by definiion We assume ha all he elecrons have he same drif velociy vd and ha he curren densiy J is uniform In a ime inerval d each elecron moves a disance v d The volume is hen Av d and he number of elecrons is nav d Elecron Drif Velociy (3) Each elecron has charge e so ha he charge dq ha flows hrough he differenial area in ime d is dq = nev d d And he curren is i = dq d = nev A d The curren densiy is J = i A = nev d The curren densiy and he drif velociy are parallel vecors, poining in he same direcion, and we can wrie J = ne ( ) v d February 3, 2005 Physics for Scieniss&Engineers 2 11 February 3, 2005 Physics for Scieniss&Engineers 2 12 3
Elecron Drif Velociy (4) Consider a wire carrying a curren The physical curren carriers are negaively charged elecrons These elecrons are moving o he lef in his drawing However, he elecric field, curren densiy, drif velociy, and curren are all o he righ because of he convenion ha hese quaniies refer o posiive charges Resisance and Resisiviy Some maerials conduc elecriciy beer han ohers If we apply a given volage across a conducor, we ge a large curren If we apply he same volage across an insulaor, we ge lile curren The propery of a maerial ha describes is abiliy o conduc elecric currens is called he resisiviy, ρ The propery of a paricular device or objec ha describes i abiliy o conduc elecric currens is called he resisance, R February 3, 2005 Physics for Scieniss&Engineers 2 13 February 3, 2005 Physics for Scieniss&Engineers 2 14 Resisance and Resisiviy (2) If we apply an elecric poenial difference V across a conducor and measure he resuling curren i in he conducor, we can define he resisance R of ha conducor as R = V i The uni of resisance is vol per ampere In honor of German physicis George Simon Ohm (1789-1854) resisance has been given he uni ohm, Ω 1 = 1 V 1 A Resisance and Resisiviy (3) The resisance of a conducor can depend on he direcion he curren flows in he conducor For example, semiconducors We will assume ha he resisance of he device is uniform for all direcions of he curren. The resisance of a conducor depends on he maerial from which he conducor is consruced as well as he geomery of he conducor Firs we discuss he effecs of he maerial of he conducor and hen we will discuss he effecs of geomery on resisance. February 3, 2005 Physics for Scieniss&Engineers 2 15 February 3, 2005 Physics for Scieniss&Engineers 2 16 4
Resisiviy The conducing properies of a maerial are characerized in erms of is resisiviy We define he resisiviy, ρ, of a maerial in erms of he magniude of he applied elecric field, E, and he magniude of he resuling curren densiy, J, as = E J The unis of resisiviy are V $ # m % & = Vm A $ A = 'm # % & m 2 February 3, 2005 Physics for Scieniss&Engineers 2 17 Typical Resisiviies The resisiviies of some represenaive conducors a 20 C are lised in he able below Maerial Resisiviy (m ) Resisiviy ( µ # cm ) Silver -8 1.59#10 1.59 Copper 1.72#10-8 1.72 Gold 2.44#10-8 2.44 Aluminum 2.82#10-8 2.82 Nickel 6.84#10-8 6.84 Mercury 95.8#10-8 95.8 As you can see, ypical values for he resisiviy of conducors used in wires are on he order of 10-8 Ω February 3, 2005 Physics for Scieniss&Engineers 2 18 5