Current and Resistance
PHY2054: Chapter 17
1
What You Will Learn in This Chapter
ÎNature
ÎDrift
of electric current
speed and current
ÎCurrent
and voltage measurements
ÎConductivity
ÎOhm’s
and resistivity
law
ÎTemperature
variations of resistance
ÎSuperconductors
ÎPower
in electric circuits
ÎElectrical
activity in the heart
PHY2054: Chapter 17
2
Current
ÎThe
electric current is defined as
‹ (a)
Amount of charge per time
‹ (b) Amount of charge per volume
‹ (c) Amount of charge per area
‹ (d) Amount of charge
‹ (e) None of these
PHY2054: Chapter 17
I=
Δq
Δt
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
‹ 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
PHY2054: Chapter 17
4
Common dry cell battery
PHY2054: Chapter 17
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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 -
PHY2054: Chapter 17
6
Direction of the current
ÎIn
conductors, electrons are free and carry the charge
ÎBut
direction of current is defined as flowing from the
positive to the negative terminal
+++
PHY2054: Chapter 17
---
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
Ne =
1 coulomb
1.6 ×10−19
= 6.2 × 1018 electrons
PHY2054: Chapter 17
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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
ÎTotal
-
-
-
-
I
charge ΔQ in volume element moving past a point
ΔQ = ( ne AΔx ) q
ÎIf
charges move with average drift speed vd, Δx = vd Δt
ΔQ = ( ne Avd Δt ) q
ÎThus,
current can be written in terms of basic quantities
i=
ΔQ
= ne qAvd
Δt
PHY2054: Chapter 17
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Example of Drift Speed
Î10A
flowing through a copper wire of diameter 2mm
‹ Density
of Cu = 8.92 g/cm3 = 8920 kg/m3
‹ 1 free electron per Cu atom
‹ Atomic mass ACu = 63.5
ÎFind
‹e
drift speed vd using i = ne eAvd
is 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 = number density of Cu atoms
ρCu
mCu
×1 =
8920
63.5 × 10−3 / 6.02 ×1023
= 8.46 × 1028 /m3
PHY2054: Chapter 17
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Example of Drift Speed (cont.)
ÎSolve
for electron drift speed vd
i
10
=
= 2.4 × 10−4 m/s
vd =
ne eA 8.46 × 1028 1.6 × 10−19 3.14 × 10−6
(
ÎThus
ÎThis
)(
)
vd is 0.24 mm/sec: ~1 hour to move 1 m
ÎCalculate
vrms
)(
thermal speed vrms
1 m v2
2 e rms
= 32 k BT
T ≅ 300K
3k BT
3 ×1.38 × 10−23 × 300
5
1.17
10
m/s
=
=
=
×
−
31
me
9.11×10
is ~ 5 × 108 times larger than drift speed!
PHY2054: Chapter 17
11
Electrons in the Wire
Î
If the electrons move so slowly through the wire, why
does the light go on right away when we flip a switch?
1.
2.
3.
4.
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
Think of what happens when you turn on a hose full of water. Water at
end of hose comes out immediately because of push by pressure wave.
PHY2054: Chapter 17
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Electrons in the Wire, Part 2
Î
Okay, so the electric field in a wire travels quickly. But,
didn’t we just learn that E = 0 inside a conductor?
1.
2.
3.
4.
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
PHY2054: Chapter 17
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Resistance and Ohm’s Law
ÎOhm’s
law is an empirical observation: for most materials
the current is proportional to the applied voltage
I ∝ ΔV
ÎWe
write the constant of proportionality as R and call it
the “resistance”, measured in ohms (Ω)
ΔV = IR
ÎExample,
‹R
120 V applied to a material gives I = 15 A.
= 120/15 = 8Ω
ÎMost
materials are “ohmic”, i.e. obey Ohm’s law over a
very wide range of applied voltages
‹ Common
“nonohmic” materials are semiconductors such as silicon
& germanium for which current rises exponentially with ΔV
PHY2054: Chapter 17
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