Current and Resistance
PHY2049: Chapter 26 1 What You Will Learn in This Chapter
ÎNature of electric current
ÎDrift speed, current and current density
ÎCurrent and voltage measurements
ÎConductivity and resistivity
ÎOhm’s law
ÎTemperature variations of resistance
ÎSuperconductors
ÎPower in electric circuits
ÎElectrical activity in the heart
PHY2049: Chapter 26 2 The electric current is defined as
ÎAmount of charge per time
ÎAmount of charge per area
ÎAmount of charge per volume
ÎAmount of charge
PHY2049: Chapter 26 3 EMF
ÎEMF device performs work on charge carriers Converts energy to electrical energy Moves carriers from low potential to high potential Maintains potential difference across terminals ÎVarious types of EMF devices Battery Electrolytic reaction Generator Magnetic field Fuel cell Oxidation of fuel Solar cell Electromagnetic energy Thermopile Nuclear decay ÎExample: 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
ÎConnecting the terminals of a battery across device leads to an electric circuit Charge begins to flow: electric current Δq I = Units: 1 Coulomb/s = 1 Ampere (A) Δ t
ÎSymbol: or +- + V -
PHY2049: Chapter 26 6 Direction of the current
ÎIn 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
ÎConsider a current of 1A. Find the number of electrons flowing past a point per second
Δq =⇒1 A 1 coulomb / sec Δt
ÎSo, in one second, number of electrons passing a point is
1 coulomb 18 Ne ==×6.2 10 electrons 1.6× 10−19
PHY2049: Chapter 26 8 Current and Electron Drift Speed
ÎConsider a material where current (electrons) is flowing Let n = # free charge carriers / m3 e A - - Let q = charge per charge carrier - - - Let A = cross sectional area of material Δx ÎTotal charge ΔQ in volume element moving past a point
Δ=QnAxq()e Δ using ΔVAx=Δ
ÎIf charges moving with drift speed vd, then Δx = vd Δt
Δ=QnAvtq()ed Δ ÎThus, current can be written in terms of basic quantities ΔQ inqAv== Δt ed
PHY2049: Chapter 26 9 Example of Drift Speed
Î10A flowing through a copper wire of diameter 2mm Density of Cu = 8.92 g/cm3 1 free electron per Cu atom
Atomic mass ACu = 63.5
ÎFind drift speed vd using ineAv= ed
−19 e is electron charge e =1.6× 10 2 23−− 62 Find A: Ar==×π 3.14( 10) =× 3.14 10 m
3 Still need ne = density of electrons (#/m ) ρ 8.92× 103 n =×=Cu 1 =× 8.5 1028 / m 3 e −323 mCu 63.5×× 10 / 6.02 10
PHY2049: Chapter 26 10 Example of Drift Speed (cont.)
ÎSolve for electron drift speed vd i 10 v == =×2.4 10−4 m/s d 28−− 19 6 neAe ()()()8.5×× 10 1.6 10 3.14 × 10
ÎThus vd is 0.24 mm/sec: ~1 hour to move 1 m
ÎBut electrons actually move ~ 106 m/s in material! This is ~ 4 × 109 times larger than drift speed
PHY2049: Chapter 26 11 Electrons in the Wire
ÎIf 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 ÎOkay, 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
I JJ≡="current density" (A/m2 ) A
Surface of area A (normal to current)
PHY2049: Chapter 26 14 Current Density Example
ÎPrevious example: I = 10 A flowing in 2mm diameter wire
2 23−− 62 Ar==×π 3.14( 10) =× 3.14 10 m
I 10 J == 3.2 × 1072 A/m A 3.14× 10−6
PHY2049: Chapter 26 15 Current Density (More General)
Id= JA⋅ Variable J, ∫S 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?
ÎI depends on material properties + shape, size of surface
ÎJ 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 non-uniform
ÎConsider equation for current and drift velocity
ineAv= ed
ÎGet current density J = i / A
Jnev= ed
Îvd has magnitude/direction at any point in space ⇒ vector
Jv= need ÎThis is “atomic-level” definition of J
PHY2049: Chapter 26 17