Physics 272
February 6
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 - 216
Summary
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Charges on all plates
have the same
magnitude
Equivalent capacitance
of a series combination
of capacitors is always
less than any individual
capacitance.
Phys272 - Spring 14 - von Doetinchem - 217
Summary
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Charges can reach capacitors independently from the source
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Imagine one big capacitor that you split into multiple smaller capacitors
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The parallel combination of capacitors always has a higher capacitance than
the individual capacitances
Charges are generally not the same on each capacitor
Phys272 - Spring 14 - von Doetinchem - 218
Energy storage in capacitors and electric-field energy
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Many important applications of capacitors rely on storing energy
Electric potential energy stored in a charged capacitor is equal to
the amount of work to separate opposite charges
Discharging of capacitor: electric field between does work
Phys272 - Spring 14 - von Doetinchem - 219
Energy storage in capacitors and electric-field energy
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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 - 220
Applications of capacitors: energy storage
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Electronic flash units in cameras
–
Capacitor is discharged when shutter button is pressed
–
Charge goes to flash tube
Capacitor can smooth out unwanted variations in
voltage surges → more in ~2 weeks
Phys272 - Spring 14 - von Doetinchem - 221
Z machine
http://www.youtube.com/watch?v=TVaIvAPMd_g
Phys272 - Spring 14 - von Doetinchem - 222
Electric field energy
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Charge a capacitor by moving electrons from one plate to the other:
work against the electric field between the plates
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Energy is stored in the field in the region between the plates
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Energy per unit volume (energy density):
Phys272 - Spring 14 - von Doetinchem - 223
Electric field energy
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Not only valid for parallel-plate capacitors
→ true for any electric field configuration in vacuum
Vacuum can have electric fields and is in this sense
not really empty
Two interpretations:
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energy is property of an electric field
–
or a shared property of all charges creating the field
Phys272 - Spring 14 - von Doetinchem - 224
Eletric field energy
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Magnitude of electric field to store 1J in a volume of
1m3
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Relation between electric field and energy density
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Dry air can sustain ~3MV/m without breaking down
Phys272 - Spring 14 - von Doetinchem - 225
Energy stored in a capacitor
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Energy stored in a capacitor
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Dielectrics
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Most capacitors have non-conducting material
between them: dielectric
Helps separating two oppositely charged conductors
Prevents ionization of the air and allows for higher
potential build up before discharges occur → store
higher energies
Phys272 - Spring 14 - von Doetinchem - 228
Dielectrics
http://www.youtube.com/watch?v=e0n6xLdwaT0
Phys272 - Spring 14 - von Doetinchem - 229
Dielectrics
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constant voltage:
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separation between plates
widened:
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plates closer together:
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electrometer shows charge flowing off of the plates
electroscope shows no change in voltage
charge flows back onto of the plates
fixed amount of charge onto left plate:
–
separation is widened
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Plexiglass inserted between the plates:
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electroscope shows a rising voltage (charge stays constant)
voltage drops
When plexi is removed
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voltage rises back up again → charge is still there
Phys272 - Spring 14 - von Doetinchem - 230
Dielectrics
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Charge stays constant
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Insert dielectric: voltage drops
C=Q/V → capacitance increases with dielectric
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Dielectric constant:
K=Cdielectric/Cvacuum
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For a given charge the potential difference is reduced by a factor
K
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K is always larger than unity
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Air has K=1.0006
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Water has K=80.4
poor conductor, but good solvent → ions dissolve in water →
current flow
Dielectrics always show some leakage (no perfect insulators)
Phys272 - Spring 14 - von Doetinchem - 231
Induced charge and polarization
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When dielectric is inserted and charge is kept
constant
→ potential difference drops
→ electric field drops
→ surface charge density drops, but not the charge
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Redistribution of charges in dielectric occurs:
polarization
Phys272 - Spring 14 - von Doetinchem - 232
Induced charge and polarization
Phys272 - Spring 14 - von Doetinchem - 233
Induced charge and polarization
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High capacitances can be reached with a dielectric
with high K value
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Capacitor with and without dielectric
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Capacitor with and without dielectric
0
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Capacitor with and without dielectric
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Field does work on dielectric to polarize
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Moving dielectric into capacitor
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Moving dielectric into capacitor
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Moving dielectric into capacitor
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Moving dielectric into capacitor
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Dielectric breakdown
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Dielectric can become a conductor
Electrons are ripped loose from atoms creates an
avalanche
→ arcing or lightning
Discharge can cause damage to capacitors and
circuits
→ conducting path allows charge to flow where it is
normally not allowed
Depends on temperature and pressure, purity of
material
Phys272 - Spring 14 - von Doetinchem - 245
Molecular model of induced charge
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Dielectric has no free charges
→ where is the induced charge coming from?
If material molecules have an electric dipole moment
→ alignment of dipoles in electric fields
If no dipoles in dielectric:
electric field induces dipoles → dipoles align in field
Phys272 - Spring 14 - von Doetinchem - 246
Gauß's law in dielectrics
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Calculation only requires knowledge of K of dielectric and
the free charge on the conductor
Phys272 - Spring 14 - von Doetinchem - 247
Review
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Any pair of insulated conductors forms a capacitor
A charged capacitor has charges of the same amount and opposite sign on
the insulated conducting sides
Capacitance is a property that defines how much charge can build up at a
certain voltage and is determined by the dimensions
Circuits with capacitors in parallel have a higher equivalent capacitance
than the individual capacitors
Circuits with capacitors in series have a lower equivalent capacitance than
the individual capacitors
Energy can be stored in the electric field between the conductors
Dielectrics between the conductors of a capacitor change the capacitance
and can be used to build elements with high capacitance
Phys272 - Spring 14 - von Doetinchem - 248
Discussion
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Suppose the two plates of a capacitor have different areas. When the capacitor is
charged by connecting it to a battery, do the charges on the two plates have
different or equal magnitude?
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The freshness of fish can be determined by placing a fish between plates of a
capacitor and measuring the capacitance. Why?
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Due to the attraction of the opposite charges on the plates, charge will be on only that part of
the larger plate that is directly across from the smaller plate. Both the capacitor and the
battery remain neutral; the two plates have charges of equal magnitude.
The capacitance depends on the dielectric constant of the fish and this in turn depends on
the amount of water in the fish’s tissue.
Liquid dielectrics that have polar molecules always have dielectric constants that
decrease with increasing temperature. Why?
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Increasing temperature increases the kinetic energy of the molecules and this decreases the
alignment of their molecular dipoles. This decreases the electric field they produce that
opposes the electric field due to the charges on the plates.
Phys272 - Spring 14 - von Doetinchem - 249