AP Physics - Electric Current

Transcription

1 AP Physics - Elecric Curren Did you ever imagine wha your paheic life, grim as i already is, would be like wihou hose lile wall socke hingees you have mouned on he wall jus above he deck of your house? Know wha he Physics Teacher is alking abou? Well, he s alking abou your basic elecriciy! People have only had elecriciy for he pas hundred years or so. Wha a difference i makes in how we live. Jus abou everyhing in he modern home works off elecriciy we make ligh, wash dishes, clean he deck, drill holes, cook food, freeze pork chops, sew clohes, cu wood, lisen o music, cool food, wach moving images, mash poaoes, dry our hair, ape T shows for laer viewing, hea air and waer, manipulae bis of informaion... he lis goes on and on. When we sudied elecric fields, we mainly deal wih charges ha weren doing much. You ginned up a bi of charge by rubbing a balloon wih a rabbi fur, and hen had fun waving he hing around, aracing bis of paper. Grea spor, bu wha good is i? Can really do any proper work wih i, can you? Well, ruh be old, saic elecriciy was no erribly useful (even hough he Physics Teacher loves i) - aside from a physics lab (where i was explored wih grea ineres) i was mainly used o enerain people during lecures or as oys. Sill, saic elecriciy, while cool and ineresing in and of iself, was no erribly useful. For one hing i was a lo of rouble. You had o rub hings or roae hings his enailed a lo of work and he payoff was raher piiful you ge a lousy spark or arac a bi of fluff o a charged up rubber sick. Big deal. Elecriciy didn really ake off and become he huge, dynamic engine of change ha ransformed he plane unil a way was found o have a coninuous flow of charge hrough a conducor. Wha was needed was a volage source. The firs volage source was wha we now call he baery. Baery Business: In he 1790 s Luigi Galvani found ha he could remove he leg of a frog (from he frog), place i on his lab able, and make i wich by ouching i wih a scalpel. This acually happened by acciden. Kind of scary don you hink? A dead leg suddenly wiching? Well, i quie caugh he fancy of Galvani. How could his be? Afer a series of experimens, he found ha he cause of he wich was a flow of charge generaed by wo dissimilar meals he scalpel and he meal lab ableop. The word galvanized remains as a ribue o Mr. Galvani. One is galvanized when he muscles suddenly conrac. Alessandro ola was inspired by his and learned o manufacure he firs we cells (he hing ha led o he modern baery). He used bis of dissimilar meals o generae elecriciy placed ino a sequence of elecrolye bearing bowls. The bowls were placed in a line and he conneced hem ogeher wih srips of meal ha were half copper and half zinc. He called his device he crown of cups. 340

2 The device produced elecriciy coninuously! As fas as you drew he elecrons off hey were replaced wih new ones. Amazing! Allesandro also developed an even beer mehod his one involved a sack of discs ha alernaed beween wo differen meals. Beween he meal discs was a cardboard disc ha had been soaked in sal waer. If he op meal disc was conneced o he boom disc wih a conducor, a coninuous flow of elecrons hrough he wire and he discs resuled. The device is called ola's pile. The uni for poenial difference, he vol, was named for ola. These primiive devices evolved ino he baeries ha we use oday dry cells (your basic alkaline energy cell ype hing) and rechargeable baeries (nickel cadmium and lead acid baeries). Properly speaking a baery is a collecion of cells. A single AA Duracell hingee is, o be correc abou he hing, called a cell, no a baery. A French physicis named George Leclanche ( ) invened he dry cell over a hundred years ago. These cells were made up from a zinc can he zinc acs as he cahode - and a carbon rod ha serves as he anode. The elecrolye is a pase made up of manganese oxide (MnO 4 ), ammonium chloride (NH 4 Cl), and powdered carbon. Modern dry cells include he alkaline ype dry cells. These are consruced much he same as he older (and cheaper) zinc carbon ypes. The main difference is he elecrolye. Boh use carbon rods and zinc cans. The elecrolye in he alkaline baery is basic raher han acidic. I urns ou ha he zinc can lass longer in a basic soluion. In his ype, he NH 4 Cl is replaced wih poassium hydroxide (KOH) or sodium hydroxide (NaOH). Boh of hese cells produce approximaely 1.5. The amoun of charge ha can be provided depends upon he size of he cell. A large D cell can produce a greaer amoun of charge han can a small AAA cell. All of hese ypes of cells or baeries are called primary cells. They produce elecriciy as long as he chemical reacions ake place. When hey cease, he baery is dead. A which poin you go ou and buy a + - anode cahode carbon rod pase of MnO 4, NH Cl, and carbon 4 zinc case 341

3 new one. You use hem and hen hrow hem away. A second major ype of cell or baery is also in use, hese are called secondary cells or sorage cells. These baeries, once hey've been drained of curren, can be recharged. Examples would be your old auomobile lead acid baery and nickel cadmium baeries used in porable elecric devices. Baeries work because of a chemical reacion ha akes place wihin he hing. These are known as oxidaion/reducion reacions. You will learn all abou hem in advanced or AP chemisry. The name is ofen shorened o redox reacions. In a redox reacion, elecrons are ransferred from one reacan o he oher. The reacan ha gains elecrons is "reduced", and he reacan ha loses elecrons is "oxidized". This causes elecrons o move from one chemical subsance o anoher. Any movemen of elecrons is called an elecric curren. Elecric Curren: Elecric curren is simply he flow of elecrons hrough a conducor. Two hings are needed for curren o flow: 1. A volage source (a dry cell will do nicely).. A complee pah hrough wich he elecrons may move. The carrier of charge in a solid conducor is he elecron. Posiive charge canno move as i is ied up in he proons of he aoms, which are essenially fixed in posiion. There are wo differen kinds of elecric curren; dc and ac. dc sands for direc curren. This is where he elecrons all flow in he same direcion. ac sands for alernaing curren. In an ac circui he direcion of he curren changes. We will deal mainly wih dc curren. To mainain he flow of elecrons - he elecric curren - a consan poenial difference mus be mainained. Such poenial differences are produced by volage sources. Common volage sources are: dry cells, baeries, generaors, magneos, solar cells, fuel cells, and alernaors jus o name a few. The symbol for elecric curren is I. (This doesn make a whole bunch of sense. You have o undersand, however, ha his convenion comes from France, so wha did you expec?) The uni for curren is he ampere, which is abbreviaed as A or amps. 1A1amp 1 C s Elecric curren is defined as he rae a which he charge flows hrough he conducor. The equaion for curren is: Q I Equaion for curren. 34

4 I is he curren in amperes, Q is he charge in Coulombs, and is he ime in seconds. Q The equaion given on he AP Physics Tes is: I Avg Q Bu we ll use I because i s easier o wrie. The ampere is a fairly large quaniy, so i is very common o use he ma. 1 ma = 10-3 A 3.5 x e - flow pas a poin in 0.35 s. Wha is he curren? We firs have o conver he number of elecrons o he charge ha hey have in Coulombs. 17 1C x 10 e 0.50 x10 C C x10 e I Q C 0.35 s 0.1 A Direcion of Curren Flow: This is an area of conroversy. Doesn seem logical ha people would argue abou his, bu hey do. The convenion ha we will use is his one. The direcion of curren flow is he direcion ha a posiive charge carrier would ravel in he circui. Now his makes no sense a all, and wise people don use i. The U.S. Navy does no use his convenion; ha s how bad i is. Anyway for us: elecriciy flows in he same direcion as posiive charge. The reason his is so supid is ha here is no posiive charge carrier. Only a negaive charge carrier, he ubiquious elecron. Acually, he only reason we use his supid convenion is ha i is he one used on he AP Physics es. So se your mind o using his supid convenion. Curren Flow Basics: The pah ha he elecrons use as hey flow around and around is called a circui. The simples possible circui would have a volage source and a conducor ha connecs he posiive and negaive side of he volage source. 343

5 As he elecrons move hrough he conducor, heir moion is blocked somewha by he aoms in he conducor, so he curren encouners a kind of opposiion o is flow. We define his as resisance. The uni for resisance is he Ohm. The symbol you ask? Okay i is his;. The hing ha uses up he elecriciy and provides he resisance is called he load. A load could be a ligh bulb, an elecric moor, a solenoid, a heaing coil, &c. The resisance of a conducor is very small, so elecrons ravel hrough i very easily. If i had a lo of resisance i would be called an insulaor. Many circuis have componens placed in hem o deliberaely add resisance. These are called resisors. For curren o flow hrough a resisor here mus be a poenial difference across i one side is a one poenial and he oher side is a anoher poenial, he elecrons flow hrough he hing aemping o equalize he poenial. We call his volage difference he volage drop. Circui Symbols: There are a number of sandard symbols ha are used when a drawing is made of a circui. These drawings are called schemaics. In old imey days elecronic devices would come wih a schemaic showing how he circui worked. You don see his much hese days, mainly because he circuiry oday is usually shrunk down and pu on a microchip. Can do much o repair a broken microchip. The symbol for a resisor is: The symbol for a baery is: + or The large line is he posiive side of he baery and he small line is he negaive side of he baery. Where you have only a large line and a small one, you have a cell. Conducors are simply sraigh lines. The symbol for a swich is: Le s look a a simple circui. I is shown in an open posiion. Which means ha i has creaed a gap in he circui so ha curren canno flow. The circui has a baery, a swich, and a resisor. The resisor represens he load on he circui. The load is he hing in a circui ha uses up he elecriciy. The load for a power plan is all he various places on he nework ha use he curren ha is produced. The load in a flashligh for example is he ligh bulb. The direcion of curren is he direcion of a posiive charge carrier. This would be from he posiive side of he baery o he negaive side of he baery. So he curren goes up (when he 344

6 swich is closed, making a complee circui), makes a righ urn, goes hrough he swich, hen urns righ, goes down, hen urns lef, ravels righ o lef hrough he resisor, hen urns righ, hen goes up and back ino he baery. Ohm s Law: We now have hree quaniies we can measure in a simple circui: volage (poenial difference), curren, and resisance. These hree quaniies are relaed o each oher by a simple formula known as Ohm s Law. I Ohm' s Law A poenial difference across a conducor causes curren o flow. The flow of he curren is opposed by he resisance of he circui. The resisance uses up some of he energy in he curren and convers i o hea. A waffle iron draws 7.1 A when plugged ino a 10 circui. Wha is is resisance? 10 I 17 I 7.1 A esisiviy: We consider shor lenghs of conducors o have essenially zero resisance, bu his is no rue for long lenghs. The resisance of a conducor is given by his equaion: l A is he resisance, is he resisiviy of he conducor, l is he lengh of he conducor, and A is he cross secional area of he conducor. This equaion is only good for wires ha have a consan cross-secion. The resisiviy depends on he meal, each meal has i own value. Generally you look he hing up when you wan o do a problem. The longer he wire, he greaer is resisance will be. Wha abou he size of he wire; is diameer? You can see from he equaion ha as he cross secional area of he wire increases, he resisance will decrease. So a hick fa wire will have less resisance han a very hin one will. Ineresing. Think of i his way, in a big fa wire here are esisiviies of Common Maerials Maerial esisiviy (m) Silver Copper Gold Aluminum Tungsen Iron Plainum Lead Nichrome Carbon Germanium Silicon Glass Hard ubber Sulfur Quarz 1.59 x x x x x x x x x x x

7 los of pahs for he elecrons o go hrough. In a skinny wire, here aren as many pahs and he elecrons are sor of scrunched ogeher rying o ge hrough, so hey ge held up more. This means more resisance. If you look a he able of resisiviy values, you see ha he bes conducor is silver wih copper coming in a close second. Silver, grea conducor ha i is, is quie expensive, so copper is he conducor of choice when wiring hings ogeher. Gold is someimes used, no because i is he bes conducor, which, from he able, you can see, bu raher because i is prey iner suff and doesn reac wih is surroundings or corrode. Copper is quie happy o corrode. So elecrical connecions wih copper wire ha is exposed o he elemens can corrode. Tha wouldn happen wih gold. Here is a lovely model of elecriciy flowing hrough a circui. We have a coal mine which pus 100 ons of coal ino each car ha goes hrough. The cars come in empy, hey leave wih coal. The mine represens he volage source. Each car receives 100 ons of poenial energy. This is equivalen of he energy provided by a baery. The rain ravels along he rack, which represens he conducor in a circui. As he cars ravel along hey pass hrough a car rae meer which measures he number of cars ha pass in a minue. This represens he curren, which is he number of Coulombs of charge per second. Here we have a rae of 5 cars/minue. each car begins wih 100 ons A Mass Difference is 100 ons Coal Mine adds 100 ons o each car 5 cars/minue each car reurns wih no coal A Car rae Meer The nex hing he rain mus ravel hrough is a coal deecor. This is he gizmo represened by This device measures Power Plan 500 ons/min he amoun of coal in each car going in and ou and measures he difference. For he firs one, he ons of coal in each car is he same going in as coming ou. This meer represens he vol meer which measures poenial difference across a componen. There is no poenial difference in a shor piece Mass Difference of conducor jus as here is no is 100 ons difference in he amoun of coal in each car raveling along he sraigh rack. No mass Difference 346

8 The coal arrives a a power plan. This, he power plan, represens he load. Each car dumps he 100 ons of coal i began wih. There is a coal mass difference across he plan of 100 ons per car. This represens he volage drop of he load. Afer he power plan, once again here is no mass difference beween he cars. Also he car rae is sill he same, 5 cars/minue. Back a he mine, here is a mass difference as he cars go ino he mine and leave he mine of 100 ons per car. This represens he volage drop across he baery. Wha a lovely lile model. Is everyhing clear? Wha if here were power plans? Wha is he resisance of a copper wire, which has a diameer of 1.00 mm and a lengh of 5 m? The resisiviy of copper is 1.7 x 10-8 m. All we have o do is plug and chug. l x10 m l A A 6.4 x m 1.00 x10 3 m Elecrical Energy & Power: A baery conains poenial energy which, when i is discharged, is convered ino he kineic energy of he elecrons. The resisance of he circui convers he kineic energy of he elecrons o hermal energy. Ever noice how warm a ligh bulb ges afer is been swiched on for a few minues? Toy ovens ha lile girls play wih acually use he hea produced by a ligh bulb o bake cookies. The circui uses up he energy provided by he volage source. We know ha elecrical poenial energy is: U q The rae a which he poenial energy is provided is he power: W U P becomes P q Bu q is he curren, I. so q q P I This gives us a simple equaion for power: 347

9 P I P is power, I is curren, and is he poenial difference. This equaion will be provided o you on he AP Physics Tes. If we apply Ohm s law o he power equaion, we can develop a few oher power equaions as well. Bu you won have hese for he es, alhough you can easily develop hem yourself. You will have Ohm s law o play around wih, so his is a useful hing. Here is he power equaion: P I Using Ohm s law, I we can plug I ino he power equaion for. P I I P I Also, from Ohm s law I So P P This gives us 3 equaions for Power: P I P I P When elecrons flow hrough a conducor, he power loss due o he resisance of he conducor is equal o I. This is called he I Loss or joule heaing. I can be very significan in long conducors. For example, power lines can have very large losses of energy o he I loss. When you buy elecriciy from he power company, you are no buying power. You are acually buying work, i.e. hey sell you energy which you do work wih. The uni ha he friendly power company sells heir energy in is no he joule. They sell i by he kilowa hour. Bu wha is a kilowa hour? 348

10 Power is he rae a which work is done: W P so W P We can ake a kilowa hour and conver i o joules. This should convince you ha i is in fac a uni of energy s10 3W J kw h s 3.6 x 10 1 h 1kW s J An elecric heaer provides 50.0 o a nichrome wire of resisance 8.0. Find he (a) curren hrough he wire and (b) power of he device. (a) We can easily find he curren in he wire using Ohm s law: I 50.0 I A (b) Find he power: 50.0 P I and I so P 310W 8.00 You have a 75 W ligh bulb. I goes ino a 10 circui. So wha is (a) he resisance of he bulb and (b) he curren ha flows hrough i? (a) esisance: (b) Curren: 10 P 190 P 75W 10 I I 0.63 A 190 You wach T for.8 hours. The T is raed a 3.8 kw. If elecriciy coss 9.5 cens per kwh, how much did your lile T program cos you o wach? All we need figure ou is he number of kilowa hours used up, hen aply he 9.5 cens per kilowa hour conversion facor. W P W P 3.8 kw.8 h 10.6 kwh 9.5 cens 10.6 kwh cens $ kwh 349

11 We didn round i off o wo significan figures. This is because you jus know ha he power company would never round anyhing off (excep o round i up), he greedy blighers! An oven operaes drawing 4.0 A on a 10 household circui. If you run i for 5.0 hours, how much does i cos (a 8.0 cens a kwh)? P I 4 A W.88 kw.88 kw 5.0 h 14.4 kwh Cos: $0.08 Cos 14.4 kwh $ kwh When a coffee seed is planed, i akes five years o yield consumable frui. Our eyes are always he same size from birh, bu our nose and ears never sop growing. The whie par of your fingernail is called he lunula. A wo-bi moon is in he firs quarer. Oak rees do no have acorns unil hey are fify years old or older. Ocober 10 is Naional Meric Day. The permanen eeh ha erup o replace heir primary predecessors (baby eeh) are called succedaneous eeh. Assuming udolph was in fron, here are 4030 ways o arrange he oher eigh reindeer. If you can see a rainbow you mus have your back o he sun. If you don', you can' see i. Drinking waer afer eaing reduces he acid in your mouh by 61 percen. Source: Denianne Bland The wo mos common surgeries are biopsies and cesarean secions. Naional Pi Day is March 14, a 1:59. (3/14 1:59) The digis of pi are , he greaes sum of 7 consequive digis in he firs 1,000,000 or so digis. If you need o remember pi, jus coun he leers in each word in he senence: "May I have a large conainer of coffee?" If you ge he coffee and are polie and say "Thank you," you ge wo more decimal places. [ ] Plaser of Paris is naurally fire reardan. A abou 600 degrees Farenhei he chemical waer ha is sored in i is released. This is also why walls are ofen "sweay" afer a fire. Mos of he iamin C in fruis is in he pih (skin). 350