Download Physics 272

Physics 272
April 10
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
[email protected]
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Summary
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Resonance in alternating-current circuits
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It is important to understand how LRC circuits
depend on the angular frequency 
Example: radio signal of a certain frequency
produces greatest signal when the circuit is tuned to
this frequency
→ circuit is in resonance
Connect AC source with constant voltage and
variable frequency to LRC series circuit
–
Current has same frequency
–
Impedance depends on frequency
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Resonance in alternating-current circuits
minimum of impedance
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A minimum in impedance exists where X L and XC cancel
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Current becomes maximum at this frequency I=V/Z
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Circuit behavior at resonance
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Position of minimum impedance is called resonance
frequency
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Capacitive and inductive reactance cancel:
This is the same frequency of an ideal LC circuit
Inductive and capacitive voltages have a 180deg
phase angle
→ cancel at all times at resonance frequency
Voltage across resistor is equal to source voltage at
resonance
(circuit behaves like there are no inductors or
capacitors)
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Tailoring an AC circuit
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Resonance frequency can be
changed by changing L
and/or C
Tuning knob in old radios was
moving capacitor plates
→ change in capacitance
Source: http://commons.wikimedia.org/wiki/File:Autoradio_De_Wald.jpg
Modern approach: change L by moving ferrite core
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Tailoring an AC circuit
https://www.youtube.com/watch?v=ZYgFuUl9_Vs
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Sharp increase at
resonance frequency
current
Tailoring an ac circuit
R
Value of resistance
determines how sharp
the change is
Important for
discriminating between
different radio stations
If the peak is too sharp
→ information will be
lost
3xR
9xR
frequency
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Tuning a radio
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Resonance frequency:
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Reactances:
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Tuning a radio
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RMS current:
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Voltages:
VL, VC are both significantly larger than V R
→ they cancel at resonance (180deg phase angle)
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Transformers
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Advantage of AC
over DC electric
power distribution:
–
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Stepping voltage
levels up and down
is easy
Long distance transmission:
–
high voltages (500kV)
→ lower i2R losses at the same energy throughput
–
Thinner cables for high voltages
Safety requires that the normal user operates at
much lower voltages
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How transformers work
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AC source causes an alternating current in the primary
coil (the one that is powered)
Alternating magnetic flux in core (made of material with
high permeability)
→ induced emf in primary coil
Same alternating flux goes through secondary coil
→ also induces emf at same frequency as primary coil
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How transformers work
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Magnetic flux through both coils is the same:
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Induced emf is equal to terminal voltage if windings have zero resistance
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How transformers work
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Choice of windings determines the voltage output of
the secondary coil
Wall charger transforms 110V AC
to, e.g., 5V DC for USB
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Energy considerations for transformers
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Power delivered to the
primary coil is the same
that is taken out by the
secondary to power a
device
Not only voltages are
transformed, but also
the impedance
Real transformers
have losses due to
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non-zero resistance (transformer gets warm)
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Hysteresis in the core
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Energy considerations for transformers
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Real transformers have losses due to
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Magnetic field is constantly changing
→ eddy currents build up
→ energy wasted
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Use laminated cores to narrow
path for eddy-currents
→ smaller radius → lower opposing magnetic field
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Magnetic flux in each path is much
smaller
Transformers typically reach
efficiencies of greater than 90%
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Review
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Root-mean-squares of sinusoidal voltages and
currents for
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Resistance and reactance:
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Impedance:
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Power in an AC circuit:
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Review
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Resonance in an AC circuit
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Transformers:
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Electromagnetic waves
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What is light?
→ electromagnetic wave
→ electromagnetism is needed
(not the complete story → QFT)
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Time varying magnetic field creates electric field
Time varying electric field creates magnetic field
→ sustain each other and create an
electromagnetic wave that propagates through
space
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Electromagnetic waves
Source: http://en.wikipedia.org/wiki/Light
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Electromagnetic waves carry energy and momentum
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Electric and magnetic fields in sinusoidal waves have defined frequency
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Infrared, visible light, UV, X-ray, -ray, etc. all follow the same principle,
but at different wavelength
Electromagnetic waves do not require medium (like mechanical waves)
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Electricity, magnetism, and light
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Maxwell's equation relate magnetic and electric field
Moving charges produce both electric and magnetic
fields
An electromagnetic wave is formed when a charge
accelerates
We never spoke about how fast a magnetic field can
be measured at a certain distance after a charge
starts moving:
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Electromagnetic waves do not travel with infinite speed
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Generating electromagnetic radiation
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Look at oscillating L-C circuit
Transformation of the LC circuit into a conducting
rod:
→ this is still an oscillating LC circuit
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Generating electromagnetic radiation
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What do the electric and magnetic fields look like:
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In initial configuration fields are contained in capacitor and inductor
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In the rod configuration the electric and magnetic field overlap
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Current is moving up and down the rod
→ charge in “capacitor” and current in “inductor” are changing with
time
→ electric and magnetic field change with time
→ electric and magnetic field propagate with finite velocity
→ electromagnetic wave
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Hertzian dipole
Source: http://de.wikipedia.org/wiki/Hertzscher_Dipol
Change of electric field over time
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Plane electromagnetic waves
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Make the following assumption:
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Electric and magnetic field configuration with wave-like
behavior
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Electric field has only a y component
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Magnetic field has only a z component
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Both move in x direction with velocity c
We have to test if
this assumption is
consistent with
Maxwell's
equation
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