Transcript 1700_voltage_2012aug06

III. Voltage
Dr. Bill Pezzaglia
Updated 2012Aug06
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A. Voltage
1) Electrostatic Energy
2) Electric Potential (Voltage)
3) Capacitance
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1. Electrostatic Potential Energy
a) Review Gravitational Potential Energy
b) Electrostatic Potential
a) Review: Gravitational Potential Energy
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• Near surface of earth, where gravitational field is constant g=9.8
m/s2, then the change of potential energy of lifting a mass “m” up
a distance “h” is just: U=mgh
• For large distances, gravity follows the inverse square law. A
body “m” falling from infinity to the surface of the earth (mass
“M”) will have a change of potential energy of:
Mm
U  G
R
• This would be the amount of energy
that a meteor would have hitting the
earth and making a big crater!
b) Electrostatic Potential Energy
• Electric fields also follow the inverse square law.
Hence a small test charge “q” pushed from infinity
onto a massive ball of charge “Q” of radius “R” will
have a change of potential energy of:
qQ
U   k
R
Note: energy of two positive (or two negative) charges is positive
Energy of positive and negative charge is negative
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2. Voltage
a) Definition of Voltage
b) Sources of Voltage
c) Measuring Voltage
2a. Definition of voltage
• Potential Energy per unit test charge:
(i.e. don’t want test charge to affect field)
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U 
V  Lim 
q 0
q
• Units: Volt=Joule/Coulomb
• Voltage is the “pressure” that makes charges
move (current flow).
• Even if there is no test charge to experience it,
voltage exists
2ai. Cathode Ray Tube
•
A CRT (Cathode Ray Tube) is a
vacuum tube with a large voltage
across the electrodes. Electrons are
emitted by the Cathode and
accelerate towards the anode.
•
Kinetic energy the electrons gain is
hence: U=e V
•
1 eV = 1 electron volt is the energy of
one electron accelerated through one
volt = 1.6x10-19 Joules.
http://www.youtube.com/v/XU8nMKkzbT8?f=videos&app=youtube_gdata&autoplay=1
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2aii. Particle Accelerators
SLAC (Stanford
Linear Accelerator
Center) accelerates
electrons to 50 GeV
of energy
Note: the E=mc2
rest-mass energy of
a proton is only 938
MeV
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2b. Sources of Voltage
(a) Point Charge Source
(b) Superposition of Point Charges
(c) Batteries
(d) Thermo and Piezoelectrics
2bi. Charge as Source of Voltage
• Define the voltage at infinity to be zero
• Voltage a distance “r” from the center of a
spherical charge Q is:
Q
V (r )  k
r
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2bii. Batteries are a source of voltage
• Volta (1745-1827) “The
Newton of electricity”
•1800 develops first battery
(approximately 30 volts)
•By adding batteries together
in series, one can make as
big as voltage as you want.
http://www.corrosion-doctors.org/Biographies/VoltaBio.htm
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2biii. Piezoelectrics etc
Some devices that are useful as detectors
• Thermoelectrics: some materials will
create a voltage across them due to a
temperature difference
• Pyroelectrics: heating some materials
will create a voltage across them
• Piezoelectrics: 1880 Pierre Curie
demonstrates effect that some crystals
generate a voltage when deformed
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2c. Measuring Voltage
Put a “voltmeter” in
parallel with element you
wish to measure
potential difference
2cii. Oscilloscope
• Oscilloscopes are used to measure voltage (especially of
AC signals). They are essentially a CRT tube with
deflection plates.
• The amount of deflection of the beam is proportional to
the voltage across the plates.
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