Current and Resistance PHY2049: Chapter 26 1
What You Will Learn in This Chapter Nature of electric current Drift speed, current and current density Current and voltage measurements Conductivity and resistivity Ohm s law Temperature variations of resistance Superconductors Power in electric circuits Electrical activity in the heart PHY2049: Chapter 26 2
The electric current is defined as Amount of charge per time Amount of charge per area Amount of charge per volume Amount of charge PHY2049: Chapter 26 3
EMF EMF device performs work on charge carriers Converts energy to electrical energy Moves carriers from low potential to high potential Maintains potential difference across terminals Various types of EMF devices Battery Generator Fuel cell Solar cell Thermopile Electrolytic reaction Magnetic field Oxidation of fuel Electromagnetic energy Nuclear decay Example: battery Two electrodes (different metals) Immersed in electrolyte (dilute acid) One electrode develops + charge, the other charge PHY2049: Chapter 26 4
Common dry cell battery PHY2049: Chapter 26 5
Electric Current Connecting the terminals of a battery across device leads to an electric circuit Charge begins to flow: electric current Units: 1 Coulomb/s = 1 Ampere (A) I = Δq Δ t Symbol: + or V + PHY2049: Chapter 26 6
Direction of the current In conductors, electrons are free and carry the charge But direction of current is defined as flowing from the positive to the negative terminal So current points in opposite direction from electron movement I +++ In the wire, electrons move very slowly (0.05 mm/s). ~ 1 meter per 5 hours!! PHY2049: Chapter 26 7
Example of Electron Flow Consider a current of 1A. Find the number of electrons flowing past a point per second Δ q = 1 A 1 coulomb / sec Δt So, in one second, number of electrons passing a point is N e 1 coulomb 18 = = 6.2 10 electrons 19 1.6 10 PHY2049: Chapter 26 8
Current and Electron Drift Speed Consider a material where current (electrons) is flowing Let n e = # free charge carriers / m 3 Let q = charge per charge carrier Let A = cross sectional area of material Δx Total charge ΔQ in volume element moving past a point ( ) Δ Q= n AΔx q e If charges moving with drift speed v d, then Δx = v d Δt ( ) Δ Q= n Av Δt q e d Thus, current can be written in terms of basic quantities ΔQ i = = neqav Δt d using Δ V = AΔx A PHY2049: Chapter 26 9
Example of Drift Speed 10A flowing through a copper wire of diameter 2mm Density of Cu = 8.92 g/cm3 1 free electron per Cu atom Atomic mass A Cu = 63.5 Find drift speed v d using i = n eav e d e is electron charge e = 1.6 10 19 Find A: A ( ) 2 2 3 6 2 = π r = 3.14 10 = 3.14 10 m n e Still need n e = density of electrons (#/m 3 ) ρcu 8.92 10 = 1 = = 8.5 10 / m m 3 23 63.5 10 / 6.02 10 Cu 3 28 3 PHY2049: Chapter 26 10
Example of Drift Speed (cont.) Solve for electron drift speed v d v d = i 10 4 2.4 10 m/s nea = = e ( 28 )( 19 )( 6 8.5 10 1.6 10 3.14 10 ) Thus v d is 0.24 mm/sec: ~1 hour to move 1 m But electrons actually move ~ 10 6 m/s in material! This is ~ 4 10 9 times larger than drift speed PHY2049: Chapter 26 11
Electrons in the Wire If the electrons move so slowly through the wire, why does the light go on right away when we flip a switch? Household wires have almost no resistance The electric field inside the wire travels much faster Light switches do not involve currents None of the above Like a hose full of water when you turn on the faucet PHY2049: Chapter 26 12
Electrons in the Wire, Part 2 Okay, so the electric field in a wire travels quickly. But, didn t we just learn that E = 0 inside a conductor? True, it can t be the electric field after all!! The electric field travels along the outside of the conductor E = 0 inside the conductor applies only to static charges None of the above EMF source constantly replenishes E field PHY2049: Chapter 26 13
Current Density Uniform current J I J = A 2 "current density" (A/m ) Surface of area A (normal to current) PHY2049: Chapter 26 14
Current Density Example Previous example: I = 10 A flowing in 2mm diameter wire A ( ) 2 2 3 6 2 = π r = 3.14 10 = 3.14 10 m J I 10 = = 3.2 10 A/m A 6 3.14 10 7 2 PHY2049: Chapter 26 15
Current Density (More General) I = J d A S Variable J, curved surface J Difference between I and J: I depends on overall geometry J(x) is a local quantity defined at any point in space S PHY2049: Chapter 26 16
Why Use Current Density? I depends on material properties + shape, size of surface J depends only on properties at a point in space J(x) depends on material properties and E field at point x Useful when shape is complex or applied field is nonuniform Consider equation for current and drift velocity i = n eav e d Get current density J = i / A J = n ev e d v d has magnitude/direction at any point in space vector J = nev e d This is atomiclevel definition of J PHY2049: Chapter 26 17