Videos
SP212
500kV line opened under load Corona Discharge
http://youtu.be/IR5HykmiIxI
Back to the Future 1.21 GigaWatts
http://youtu.be/f-77xulkB_U
Current Explained (bad digital video, good concepts)
http://youtu.be/sOc40J9YITo
Demonstration of Power Lines and
E Fields (end) http://demonstrations.wolfram.com/
ElectricAndMagneticFieldsNearATransmissionLine/
Ch. 26 – Current and Resistance
Maj Jeremy Best USMC
Physics Department, U.S. Naval Academy
February 23, 2016
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
1 / 26
Find the Physics
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
2 / 26
Electric Current
A metallic wire (like copper) has free electrons,
(conduction electrons) that are always moving, on the
order of 106 m/s.
Free electrons pass through a hypothetical plane in
both directions at the rate of many billions per
second.
There is no net transport of charge and thus no
current unless a potential difference ∆V is present.
The leads of a battery represent a potential
difference , which would cause the free electrons to
flow in a specific direction, resulting in a net
transport of charge.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
3 / 26
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
4 / 26
Electric Current
Current is defined as the amount of charge that passes a
hypothetical plane per unit time .
i=
dq
dt
In order to find the charge that passes through the plane
in a time interval we integrate:
Z
Z t
i dt = q
dq =
0
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
5 / 26
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
6 / 26
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
8 / 26
Current SI unit
1 coulomb per second = 1 C/s = 1 Ampere = 1A
NOTE: Arrows are drawn to indicate current on many
diagrams. −→
This is always drawn in the direction in which positive
charge carriers would move, even if the actual charge
carriers are negative and move in the opposite
direction. (Thanks Ben...)
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
7 / 26
Current Density
As with many things involving charge, we often describe
current in terms of current per unit area.
Z
~
i = ~J · d A
If the current is uniform across the surface and parallel
~ then ~J is also uniform and parallel yielding:
to d A
Z
Z
i = J dA = J dA = JA
so
J=
i
A
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
9 / 26
The Speed of Electricity
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
10 / 26
Drift Speed
We all know electricity moves pretty fast, right? Ever
been shocked? Let’s figure out how fast that moves.
q
t
The total charge q in the wire is the number of charges
per unit volume, times the volume, times the charge
i=
Problem: Ramming Speed!!!
We have a wire of cross sectional area
A, uniform current density ~J, applied
electric field ~E, and length L. We want
to figure out the drift speed vd of the
charge carriers in the wire.
q = nALe
And the time is the distance they travel, divided by their
speed
t=
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
February 23, 2016
11 / 26
L
vd
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
12 / 26
Drift Speed
Drift Speed
Put that all together:
OK, can we use that?
q
t
nALe
i=
L/vd
i
J
vd =
=
nAe
ne
Problem: Tokyo Drift
What is the drift speed of the electrons in a copper wire
of radius r = 900 µm carrying a uniform current
i = 17 mA?
The density of copper is ρ = 8.96 × 103 kg/m
Most of this is simple plug n’ chug, but we need our
chemistry to figure out the electrons per unit volume, n
i=
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
13 / 26
Drift Speed, calculated
February 23, 2016
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February 23, 2016
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Drift Speed, calculated
Solution:
Assume that each atom of copper gives us one single
electron.
Solution:
n = 8.49 × 1028 m−3
atoms
unit volume
atoms moles mass =
mole
unit mass
unit volume
NA ρ
=
M
(6.02 × 1023 mol−1 )(8.96 × 103 kg m−3 )
=
63.54 × 10−3 kg mol−1
n=
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
Now that we have n, we’re back to basics:
J
ne
i
=
Ane
m
mm
= 4.9 × 10−7 = 1.8
s
h
vd =
15 / 26
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
WAIT!!
We have always thought that electricity moves really
really fast...
What is up with this?
Resistance
Objects have resistance , people have resistance ,
components have it too. Resistance is defined as:
R=
V
i
The SI unit for resistance is the ohm (Ω) .
1
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
17 / 26
Resistivity
Volt
= 1Ω
Amp
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
18 / 26
Resistivity
The general properties of a material , is related by
resistivity . There is a significant difference between
resistance and resistivity. Resistivity is symbolized with ρ:
We sometimes speak instead of the conductivity, σ of a
material:
σ = 1/ρ
Of course, the resistance of a specific object is related to
the resistivity of the material from which it is
constructed:
E
ρ=
J
The units of ρ are the ohm-meter, Ω m
R =ρ
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
19 / 26
Length
Area
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
20 / 26
Temperature Dependence
Ohm’s Law
Finally, resistivity depends on temperature:
ρ − ρ0 = ρ0 α(T − T0 )
Where T0 is a reference temperature, (usually around
300 K) and ρ0 is the resistivity at that temperature. α is
called the temperature coefficient of resistivity.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
21 / 26
Ohm’s Law is an assertion that the current
through a device is ALWAYS directly proportional to
the potential difference applied to the device.
A conducting device obeys Ohm’s Law when the
resistance of the device is independent of the
magnitude and polarity of the applied potential
difference.
A conducting material obeys Ohm’s Law when the
resistivity of the material is independent of the
magnitude and direction of the applied electric field.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
22 / 26
Find the Physics (revisited)
J
C
Power = 1 V · A =
=
C
s
J
=1W
s
Why are these lines so thick? Why are they so far apart?
Power!!
P = iV
P = i 2R
V2
P=
R
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
23 / 26
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
24 / 26
Semiconductors
Are a class of elemental materials that are
somewhere in between conductors and insulators.
Silicon and Germanium are Column IV
Semiconductors.
The newest class of elemental semiconductors are
called III-V because they are combinations of
Columns III and V like Gallium (Ga) and Arsenic
(As) to form Gallium Arsenide, or Aluminum and
Nitrogen to form Aluminum Nitride.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
Wiley Plus Homework
Chapter 26: Questions: 2, 5, 8 Problems: 2, 5, 14, 23,
38, 40, 45, 49.
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
26 / 26