Current and Resistance
PHY2049: Chapter 26
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What You Will Learn in This Chapter
ÎNature
ÎDrift
of electric current
speed, current and current density
ÎCurrent
and voltage measurements
ÎConductivity
ÎOhm’s
and resistivity
law
ÎTemperature
variations of resistance
ÎSuperconductors
ÎPower
in electric circuits
ÎElectrical
activity in the heart
PHY2049: Chapter 26
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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
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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
‹ Generator
‹ Fuel
cell
‹ Solar cell
‹ Thermopile
ÎExample:
Electrolytic reaction
Magnetic field
Oxidation of fuel
Electromagnetic energy
Nuclear decay
battery
‹ Two
electrodes (different metals)
‹ Immersed in electrolyte (dilute acid)
‹ One electrode develops + charge, the other – charge
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Common dry cell battery
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Electric Current
ÎConnecting
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)
ÎSymbol:
+ -
or
Δq
=
I
Δt
+ V -
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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!!
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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
Ne =
1 coulomb
1.6 ×10−19
= 6.2 × 1018 electrons
PHY2049: Chapter 26
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Current and Electron Drift Speed
ÎConsider
a material where current (electrons) is flowing
‹ Let
ne = # free charge carriers / m3
‹ Let q = charge per charge carrier
‹ Let A = cross sectional area of material
A
-
-
-
-
Δx
ÎTotal charge ΔQ in volume element moving past a point
ΔQ = ( ne AΔx ) q
ÎIf
using ΔV = AΔx
charges moving with drift speed vd, then Δx = vd Δt
ΔQ = ( ne Avd Δt ) q
ÎThus,
current can be written in terms of basic quantities
i=
ΔQ
= ne qAvd
Δt
PHY2049: Chapter 26
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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
‹e
drift speed vd using i = ne eAvd
is electron charge
‹ Find
‹ Still
ne =
A:
e = 1.6 ×10−19
(
A = π r = 3.14 × 10
2
−3
)
2
= 3.14 × 10−6 m 2
need ne = density of electrons (#/m3)
ρCu
mCu
×1 =
8.92 ×103
63.5 ×10−3 / 6.02 × 1023
PHY2049: Chapter 26
= 8.5 × 1028 / m3
10
Example of Drift Speed (cont.)
ÎSolve
for electron drift speed vd
i
10
=
= 2.4 × 10−4 m/s
vd =
ne eA 8.5 ×1028 1.6 × 10−19 3.14 × 10−6
(
ÎThus
ÎBut
)(
)(
)
vd is 0.24 mm/sec: ~1 hour to move 1 m
electrons actually move ~ 106 m/s in material!
‹ This
is ~ 4 × 109 times larger than drift speed
PHY2049: Chapter 26
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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
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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
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Current Density
Uniform current
I
J≡
J = "current density" (A/m 2 )
A
Surface of area A
(normal to current)
PHY2049: Chapter 26
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Current Density Example
ÎPrevious
example: I = 10 A flowing in 2mm diameter wire
(
A = π r = 3.14 × 10
2
−3
)
2
= 3.14 × 10−6 m 2
I
10
7
2
J= =
3.2
10
A/m
×
A 3.14 ×10−6
PHY2049: Chapter 26
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Current Density (More General)
I = ∫ J ⋅ dA
S
J
Variable J,
curved surface
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
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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
i = ne eAvd
ÎGet
current density J = i / A
J = ne evd
Îvd
has magnitude/direction at any point in space ⇒ vector
J = ne ev d
ÎThis
is “atomic-level” definition of J
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