(1) i have completed at least 50% of the reading and study- guide assignments associated with the...
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(1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule.
a) True b) False
iClicker Quiz
Pieter van Musschenbroek (1692-1761) – University of Leyden (Holland)
“I would like to tell you about a new but terrible experiment, which I advise you never to try yourself, nor would I, who experienced it and survived by the grace of God, do it again for all the kingdom of France.”
http://s.bourdreux.free.fr/cabinet_Sigaud/chronologie/musschenbroek.htm
http://physics.kenyon.edu/EarlyApparatus/Electricity/Condenser/Condenser.html
+-
http://www.howstuffworks.com www.wikipedia.com
William Watson (1715-1787)
http://www.codecheck.com/cc/BenAndTheKite.html
Quasi-uniform field between two parallel-plates
E
VCQ
Fk
x
1
Stretch a spring
Charge a capacitor
How much charge does one Volt buy you?If the capacitance is high, one Volt goes a long ways.
Capacitance is like flexibility:
V
The SI unit of capacitance is the Farad = Coulomb/Volt.
The parallel-plate capacitor
Potential difference: V
E A
QddEV
d
00
dsE
Given A and d, if we now double the voltage, the capacitance will(1) increase by a factor of two, (2) decrease by a factor of two, (3) stay the same.
00
)/(
AQ
E
d
A
V
QC 0
If V doubles, then I also doubles. C doesn’t depend on V or I.
(1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule.
a) True b) False
iClicker Quiz
ab
ab
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kV
QC
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r
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b
a
d
0
20
41
11
dsE
abV
LQLC
a
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r
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a
b
a /ln
2//ln
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212121 CC
V
Q
V
Q
V
V
QC tot
eq
Ceq is larger than either C1 or C2.
1
212121
111
CCQV
QVVV
Q
V
QC
toteq
Ceq is smaller than smallest of C1 and C2.
Reduction of a capacitive network
C C
C C
C C C
C C
C
C
C/2
C/2
2C
C1 C2
C3C4
C5
a b
Network capacitance depends on which two points you choose to measure between.
Much harder (needs matrix methods)
a
b
b
C1 C2
C3C4
C5
Easy: 54321 )||()||( CCCCCCab
C5))C4(C3 C2C5)(C3 (C4 C1C5))(C4 C2C5 (C4 C3
C5)C4(C3 C2C5)C4(C3 C1C5 C4)(C3
abC
Energy storage in Capacitors Dielectrics Dipoles
C
QCVdUU
22
2
1
2
1
Electric potential energy stored in a capacitor
Potential difference: V
E
CVQ
CVdVVCdVVdQdU )(
Charging: initial Q and V are zero.
The first dQ is easy. But as V increases, each dQ is a little more expensive.
Potential difference: V
E
Energy density in an electric field
202
1
2
021
202
1221 )/(
Volume
EnergyE
d
V
Ad
VdA
Ad
CVu
C
QCVU
22
2
1
2
1
Force between the plates of a parallel-plate capacitor?
Quiz: The two plates of a capacitor should experience a force that is:(1) attractive (2) repulsive (3) zero.
Remember that F = dU/dx, which means that the force will act to lower the electrical potential energy.
x
AC 0
Need to hold either Q or V constant!
E
x
V
constant Q attractive constant V repulsive
Ep
Err
ErEr
FrFr
Frττ
)( 21
21
2211
q
iii
ii
d
Which way does torque vector point in this figure? Use the RHR.
Rotation aligns the moment vector (p) with the field?
Ep
θτ
)cos()sin(2/
2/2/
pEdpE
dτdU
Dielectric materials contain polar molecules that can align with an external field. The field produced by these dipoles gets added to the external field.
1,00
water
Many types of capacitors
Tubular:most common
low Q and low V
Oil:high V
Electrolytic:common
polarizeedlarge Q at small V
Ultracapacitors (a.k.a. supercapacitors)
http://en.wikipedia.org/wiki/electric_double-layer_capacitor
Huge internal A. Very small d between + and Extraordinarily-high Q and u, but low V
0QQ
dAE
Adding a dielectric to any situation
00
d
A
d
AC ppc
0
202
1221 EEu
d
AC
V
Q 0Parallel-plate capacitor with dielectric:
202
1 Evol
Uu
C
QCVU
22
2
1
2
1
d
VE
Constant Q: How do (A,d,) affect V, E, U and u?
C V E U u
d C V E U u A C V E U u
Constant V: How do (A,d,) affect Q, E, U and u?
C Q E U u
d C Q E U u A C Q E U u
d
AC
V
Q 0Parallel-plate capacitor with dielectric:
202
1 Evol
Uu
C
QCVU
22
2
1
2
1
d
VE
Quiz: Double A at constant Q. What happens to U?
(1) doubled (2) quadrupled (3) unchanged (4) halved (5) quartered
Quiz: Double at constant V. What happens to E?
(1) doubled (2) quadrupled (3) unchanged (4) halved (5) quartered
111 VCQ 222 VCQ
V1 V2C1 C2
+ +
+ + C1 C2
111 VCQ 222 VCQ
+ +
+ +
C1 C2
111 VCQ 222 VCQ
+ + + +
Crossed capacitor problem
C1 C2
21
21
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''
CC
C
QV
'''' 2211 VCQVCQ
111 VCQ 222 VCQ
V1 V2C1 C2
+ +
+ + C1 C2
111 VCQ 222 VCQ
+ +
+ +
Suppose you do the same thing without crossing them.
C1 C2
21
21
'
''
CC
C
QV
'''' 2211 VCQVCQ
C1 C2
111 VCQ 222 VCQ
+ +
+ +
Crossed capacitor problem: special case where V1 = V2
VCQ 11 VCQ 22
V C1 C2
+ +
+ + C1 C2
VCQ 11 VCQ 22
+ +
+ +
C1 C2
VCQ 11 VCQ 22
+ + + +
C1 C2
'''' 2211 VCQVCQ
21
21
21
21
'
''
CC
CCV
CC
C
QV
Two Capacitors in Parallel
-
ΔV+ + + + +
- - - - -
+ + + + + +
- - - - - 6V
Two Capacitors in Series
-
ΔV+ + + + ++
- - - - -
- - - - -
+ + + + +
6V
Discussion question: Two identical capacitors are connected first in parallel and then in series.
Which combination has the greater capacitance?
1. The pair in parallel
2. The pair in series
3. The two combinations have the same capacitance
C2
C4
C3C2
C3
C5 C5
C1
C2
The electrical potential energy stored in a capacitor is given by U=(1/2)CV^2. It is also given by U=(1/2C)Q^2. Is the energy really proportional to C or to 1/C, or is neither really true?
●i don't totally understand the question but i do know that both formulas are correct and therefore it would seem that U is proportional to C
●neither is really true. imagine a small capacitor and also imagine an infinitely large capacitor the is no charge on either of them there is no potential energy stored on either though one has an infinitely large capacitance.
●Really, both are true depending on which equation you use and which variables you set as constants. The reason this occurs is because these equations are equivalent, by the relationship C=Q/V. Therefore, depending on whether you set voltage or charge as a constant, you can really look at energy as proportional to either C or 1/C.
●Energy is actually proportional to the charge (Q) and potential difference (V) of the capacitor. The capacitance, C, comes into it because Q is also proportional to V, where the constant C for a particular configuration is equal to Q/V. The two expressions U=(1/2)CV^2 and U=(1/2C)Q^2, when Q/V is substituted for C, both reduce to the same expression, U= QV/2. Capacitance is itself a proportionality constant, so in a sense energy is proportional to C and 1/C, but really it is just a different way of saying it is proportional to charge and potential difference.
212121
21
CCV
Q
V
Q
V
V
QC
QQQ
tot
tot
1
212121
21
111
CCQ
V
Q
VVV
Q
V
QC
VVV
tot
tot
Ep
Err
ErEr
FrFr
Frττ
)( 21
21
2211
q
iii
ii
d
Ep
θτ
)cos()sin(2/
2/2/
pEdpE
dτdU
Dipole QuizLet the i unit vector point to the right. Let j point towards the board. Let k point up. Let an upward-pointing E-field be present in the room. A dipole moment directed along the j – i direction will experience a torque along what direction.
a) ib) jc) kd) –ie) –jf) –kg) none of these
i
k
In an electrically polarized material, one obtains extra surface charge per volt, and therefore, an increase in capacitance.
1,00
d
A
d
AC
QQdAE ppc
0
0
and
202
1
2
021
202
1221
22
)/(
Volume
Energy
2
1
2
1
Ed
V
Ad
VdA
Ad
CVu
C
QCVU
Energy density in an electric field
Shorted Capacitor Problem