Physics 272
February 11
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
Phys272 - Spring 14 - von Doetinchem - 250
Summary
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Potential energy of uncharged capacitor set to zero
Capacitance measures the ability to store energy
and charge
Charging of capacitor: charge increases and energy
increases
Less work is required to transfer charge if
capacitance is higher
Phys272 - Spring 14 - von Doetinchem - 251
Summary
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High capacitances can be reached with a dielectric
with high K value
Phys272 - Spring 14 - von Doetinchem - 252
Current
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So far: electrostatics: no motion of charges
Charges in motion from one region to another are
called an electric current
Charges in conducting path in a closed loop: electric
circuit
Transfer of electric potential energy from, e.g., a
battery to, e.g., a toaster or light bulb
Nervous system of your body is also an electric
circuit
In electrostatics: no net flow of free electrons inside
the conductor → no current
Phys272 - Spring 14 - von Doetinchem - 253
Current
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Turn on electric field inside conductor (more later)
→ charged particle in conductor feels electric force
Charged particles feel the electric force, but also
bump into the positive ions of the conducting
material → random change of motion
As result electrons move at an average drift velocity
and produce a net current (~10 -4m/s)
Electric field turns on nearly with the speed of light
(~108m/s) → electrons move all along the wire
Phys272 - Spring 14 - von Doetinchem - 254
Current
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Electric field does work on the moving charges
Kinetic energy is transferred to conductor by collisions
→ vibrational energy of ions
→ temperature increase
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In metals the moving charges are always electrons
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In ionized plasmas positive and negative ions can move
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Current is the net charge flow through an area and unit time
Phys272 - Spring 14 - von Doetinchem - 255
Conductivity of ionized water
http://www.youtube.com/watch?v=Rf2mS4J0FNg
Phys272 - Spring 14 - von Doetinchem - 256
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Different applications have a wide
range of different typical current
values
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Engine starter: ~200A
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TV: mA
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Computers: 1pA-1nA
Source: http://en.wikipedia.org/wiki/Andr%C3%A9-Marie_Amp%C3%A8re
Current
André-Marie Ampère
(1775-1836)
Phys272 - Spring 14 - von Doetinchem - 257
Current, drift velocity, current density
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Amount of charge flowing through an area:
Current in a conductor is the product of the density of moving
charged particles, the magnitude of charge of each such
particle, the magnitude of the drift velocity, and the crosssection area
Phys272 - Spring 14 - von Doetinchem - 258
Current, drift velocity, current density
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Caution: current I is a scalar and current density is a vector
→ current describes how charges flow in an extended object
→ current density describes what is going on locally
Here only: direct currents with only one direction in the whole
circuit
→ we will cover alternating currents later
Phys272 - Spring 14 - von Doetinchem - 259
Current density and drift velcoity in a wire
Phys272 - Spring 14 - von Doetinchem - 260
Resistivity
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Generally current density in
conductor depends on electric field
and the properties of the material as
a function of temperature
Ohm's law:
Source: http://de.wikipedia.org/wiki/Georg_Simon_Ohm
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Resistivity ρ of a material is the ratio of electric field
and current density
The greater the resistivity the greater the field has to be
to achieve the same current density
Phys272 - Spring 14 - von Doetinchem - 261
Resistivity
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Perfect conductors would have zero resistivity
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Perfect insulators have an infinite resistivity
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Metals have a ~10 times smaller resistivity than
insulators
Inverse of the resistivity is the conductivity
Ohm's law is not perfect and can only be applied for
certain temperature ranges
A conductor is called ohmic or linear if the resistivity
in a certain temperature range does not depend on
the value of the electric field
Phys272 - Spring 14 - von Doetinchem - 262
Resistivity and temperature
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Resistivity in a metal nearly always increases with temperature
due to more vibration of the ions in the material
Behavior over a small temperature range can be described by:
Measuring the resistivity is a sensitive measure of temperature,
e.g., thermistor use semiconductor materials
Superconductivity: sudden change to zero resistivity at cold
temperatures of certain materials: electrons flow freely without
creating heat in the conductor
Phys272 - Spring 14 - von Doetinchem - 263
Quench of superconducting magnets at CERN
Phys272 - Spring 14 - von Doetinchem - 264
Resistance
Not talking about this
type of resistance
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Current and potential difference are easier to
measure than current density and electric field
As current flow through electric potential difference
→ electric potential energy is lost
→ energy goes into the ions
Phys272 - Spring 14 - von Doetinchem - 265
Interpreting resistance
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Resistance is proportional to length and inversely proportional to
cross-section
Analogy:
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a narrow hose has more
resistance than a wide one
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a long hose has a larger
resistance than a short
one
Circuit device with a
certain resistance is
called a resistor
Common values:
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1-1,000,000Ohm
Source: http://en.wikipedia.org/wiki/Resistor
Phys272 - Spring 14 - von Doetinchem - 266
Resistance in a wire
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Take 18 gauge and 50m long copper wire from
before with 1.67A:
Phys272 - Spring 14 - von Doetinchem - 267
Electromotive force and circuits
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You need a complete circuit to have a steady
current
If a charge goes around a complete circuit it will
loose potential energy to the ions in the conductor
For a steady current a device that is pushing the
charge to a higher potential is needed:
source of electromotive force (emf)
Examples: batteries, generators, solar panels
transform, e.g., chemical, mechanical energy into
electric energy
Ideally: provide constant potential difference, not
depending on current
Phys272 - Spring 14 - von Doetinchem - 270
Electromotive force and circuits
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Ideal source of emf
brings charge to higher
potential energy level
without increasing the
kinetic energy
Charge is not used up in
a circuit and is not
accumulating in the
circuit elements. Both
sides of the terminal of a
battery have the same
current for an ideal
source of emf.
Phys272 - Spring 14 - von Doetinchem - 271
Emf in animals: electric eel
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Rebuild muscles
produce electric
potential differences
that are combined
(in series) to
produce strong
shocks (500V at
~0.8A)
cells pump positive
sodium and
potassium ions out
of the cell via
transport proteins
http://www.youtube.com/watch?v=1EEy-aXHzRI
Phys272 - Spring 14 - von Doetinchem - 272
Internal resistance
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Charges move through the material of a real source of
emf feel an internal resistance
If the internal resistance behaves like ohmic resistance:
For a real source of emf, the terminal voltage equals the
emf only if no current is flowing through the source.
Current in a circuit drops if the external resistance is
getting bigger.
Car battery delivers less current when the internal
resistance is higher at colder temperatures
Phys272 - Spring 14 - von Doetinchem - 273
Symbols for circuit diagrams
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Conductor with negligible resistance
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Resistor
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Source of emf
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Source of emf with internal resistance
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Voltmeter
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Ammeter
→ more to come on Voltmeter and
Ammeter
Phys272 - Spring 14 - von Doetinchem - 274
Source in a complete circuit
Phys272 - Spring 14 - von Doetinchem - 275
Potential changes around a circuit
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Net change in potential energy for a charge in a
complete circuit must be zero
→ algebraic sum of potential differences around a
circuit must be 0
Phys272 - Spring 14 - von Doetinchem - 276