I-1Electric Currents and Simple CircuitsElectrons can flow along inside a metal wire if there is an E-field present to push them along (recall F q E=r r). The flow of electrons in a wire is similar to the flow of water in a pipe.Definition: electric current QItD=D = rate of flow of chargeunits [ I ] = coulomb/second = 1 C / 1 s = 1 ampere (A) = "amp""It's not the voltage that kills you, it the amps." About 0.05 A is enough to kill you.If current I = 1 A in a wire, then 1 coulomb of charge flows past any point every second. In electrostatic problems, E 0=r inside a metal, but if I 0, then the situation is not static, the E-field is not zero.Electrons flow in metals, not protons, so (–) charges are moving when there is a current. The electron feel a force F e E=-r rand goes "upstream" against the E-field.The flow of (–) charge in one direction is electrically equivalent to the flow of (+) charge in the opposite direction:Last update: 1/14/2019 Dubson Phys2020 Notes, University of Colorado Ineutralplates() or (+)either way, get:+ + + + EI-2By convention, we define current I as the flow of imaginary (+) charges, when it is really (–) charges flowing the other way: (Some texts refer to I as the "conventional current" to distinguish it from the "electron current".)Example: How many electrons flow past per second when the current is 1 A? 18 119 19Q N e N I 1 A 1 C / sI 5.6 10 st t t e 1.6 10 C 1.6 10 C-- -D D � D= = � = = = = �D D D � �About 0.01 A = 10 mA flowing though your heart is lethal, yet I could grab a wire carrying 1000A and be safe! Why? Because my body has a much higher electrical resistance than the metal. The electrons prefer to flow through the metal wire.For most materials, the current I is proportional to the voltage difference between the ends.I E (since F = q E) and V E, so I V� D � � Dr rFrom now on, we usually follow the (bad) convention and write "V" when we really mean "V".VI V ( really I V) constantI� � D � =Definition of resistance R (of a piece of wire or other material): VRI�The experimental fact that (for most materials) the ratio R = V / I is a constant, independent of Vor I, is called Ohm's Law : VR constantI= =, usually written V = I R (R constant)Units: [R] = volt / ampere = ohm () ["" is Greek letter omega]Last update: 1/14/2019 Dubson Phys2020 Notes, University of Colorado IE Ihi Vlo VVI-3Ohm's Law should be written V = I R, but the (bad) convention is to write V = I R."Ohm's Law" is not really a law, because it is not always true. For many materials, Ohm's Law isapproximately true, the resistance R is approximately constant, independent of V or I. Materials that obey Ohm's Law are called "ohmic materials". But some materials are "non-ohmic"; they donot obey Ohm's Law. The average speed of electrons in a current-carrying wire results from a competition between twoeffects: (1) the E-field, which causes an acceleration according to F q E m a= =r rr, making the electrons go faster and faster, and (2) the scattering of electrons due to impurities and thermal vibrations, which act like friction, making the electrons slow down.For typical currents in real wires, the average electron speed (often called the drift velocity) is actually quite slow, typically less than 0.1 mm/s. (Incidentally, the term drift velocity is incorrect,it should be called the drift speed.)A material with lots of electron scattering has a high resistance:Rwire << 1 , Rhuman 105 4535V 10 VI 10 A (harmless)R 10V 100 VI 10 A (painful!)R 10--= = =W= = =W 10 V safe, 100 V dangerous !The resistance R of a piece of material depends on its shape and composition.Shape: long and skinny R big short and fat R small — just like the flow of water through a pipe. Long skinny water pipes resist flow of water.Turns out that LRA�, so big L means big R, big A means small RLast update: 1/14/2019 Dubson Phys2020 Notes, University of Colorado area ALI-4LRAr= (Greek letter "rho") = resistivityResistivity depends on the material composition, not on the shape. is a measure of the scattering of electrons in that material, like viscosity of fluid in a pipe. Big means lots of scattering (friction), big resistance to flow.Units: {length lengthlengthARL�r = � [ ] = [R] length = mmaterial useCu 1.7 10-8 m house wiringAl 2.7 10-8 m power linesW (tungsten) 5.3 10-8 m (cool)60 10-8 m (hot)light bulb filamentsFe 9.8 10-8 m not used in wiringglass 10+10 m electrical insulatorSome electrical circuits symbols:A battery's job is to maintain a constant voltage difference between its terminals. It acts like a charge pump, pushing (+) charge inside the battery from the (-) side to the (+) side. This is the direction that the charges don't want to go. The battery has to do chemical work to push the charges "uphill" (toward higher electrostatic PE).Last update: 1/14/2019 Dubson Phys2020 Notes, University of Colorado resistorcapacitorbatteryswitchR CE or V(+) side(–) sideI-5A Simple Circuit"10-volt battery" means voltage across battery = E or V (or just V) = 10 volts = 10 V. Hence the confusing equation: V = 10 V, meaning "the voltage difference across battery is 10 volts".Always assume that the wires connecting circuit elements have zero resistance Rwire = 0 no voltage change along the wire, since Vwire = I Rwire = I 0 = 0.Current around the circuit is: V 10 VI 0.2 AR 50= = =WRecall that (+) charge tends toward low voltage. Can think of voltage as a kind of "electrical pressure". Water in a pipe flows from high pressure to low pressure. Likewise, (+) charges in a wire flow from hi V to lo V. In the water-pipe analogy, we can think of a resistor as like a porousplug of gravel in the pipe. The gravel plug offers resistance to the flow of water, so we need a large pressure difference to push the water through.If no pressure difference across a pipe plug, then no water flows.If no voltage difference across a resistor, then no current flows.Inside a resistor, (+) charge flows from hi V lo V ("downhill")Inside a battery, (+) charge flows from lo V hi V ("uphill").Current I is the same in the battery and the resistor, just as water flow (in gallons per minute) is same through pump and through gravel
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