summary more circuits forces between plates of a capacitor dielectrics energy and the distinction...
TRANSCRIPT
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Summary
• More circuits• Forces between
plates of a capacitor• Dielectrics• Energy and the
distinction about constant Q or V.
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C1 = 5μF, C2 = 10 μF, C3 = 2 μFCalculate the equi. Capacitance.
a) 6 μFb) 2 μFc) 4 μFd) 8 μF
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a. Find the equivalent capacitance between points a and b. b. What fraction of the total energy is stored in the 7 µF capacitor , if the circuit has been charged by a 12 volt battery?
a. 12.92 µFb. 46%
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C123 2.4 µF, q = 28.8 µC
C2 C24 = 12 µF
C1234 = 3 µF q =36 µC
Δq = 7.2 µC
C1 = C3 = 8.00 μF, C2 = C4 = 6.00 μF, V = 12VWhen the switch S is closed, how much charge flows through point P
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Question
• A parallel-plate capacitor has a plate area of 0.3m2 and a plate separation of 0.1mm. If the charge on each plate has a magnitude of 5x10-6 C then the force exerted by one plate on the other has a magnitude of about:
• A. 0 B. 5N C. 9N D. 1 x104 N E. 9 x 105 N
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Question• A parallel-plate capacitor
has a plate area of 0.3m2 and a plate separation of 0.1mm. If the charge on each plate has a magnitude of 5x10-6 C then the force exerted by one plate on the other has a magnitude of about:
A. 0B. 5NC. 0. 9ND. 1 x104 NE. 9 x 105 N
N
A
qqEF
o
71.43.01085.82
105
2
12
26
2
The electric field = σ/2εo why?
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dAC o /
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q
-q
q'
q
q
-q'
-q
-q
V
V
V
V'
In 1837 Michael Faraday investigated what happens to the
capacitance of a capacitor when the gap between the plates
is completely filled with an insulator (a.k.a. dielectri
C
Capacitor with a dielectric
c)
Faraday discovered that the new capacitance is given by :
Here is the capacitance before the insertion
of the dielectric between the plates. The factor is known
as the dielectric co
airairC CC
nstant of the material.
Faraday's experiment can be carried out in two ways:
With the voltage across the plates remaining constant
In this case a battery remains connected to the plates .
This is
V1.
shown in fig.a
With the charge of the plates remaining constant.
In this case the plates are isolated from the battery
This is shown in fig.b
q2.
airC C
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q
-q
q'
q
q
-q'
-q
-q
V
V
V
V'
airC C
This is bacause the battery remains connected to the plates
After the dielectric is inserted between the capacitor plates
the plate charge changes from tq
Fig.a : Capacitor voltage V remains constant
o
The new capacitance air
q κq q C κ κC
V V V
q q
This is bacause the plates are isolated
After the dielectric is inserted between the capacitor plates
the plate voltage changes from to
The ne
w capa
VV
V
Fig.b : Capacitor charge q remains constant
citance
/ air
q q qC C
V V V
(25 - 16)
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If the areas are A1 and A-A1.
2112 (
AAd
C o
C123 2.4 µF, q = 28.8 µC
C2 C24 = 12 µF
C1234 = 3 µF q =36 µC
212
d
AC o
Effect of a dielectric : C κC
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The force on a filling dielectric as it is inserted between the parallel plates of a capacitor.
L
Cdx
dC
L
xA
dCCC o
1
1121
x
L
With the battery connected, U1 = ½CV2
With the battery disconnected, U2 = Q2/2C
L
Udx
dUF
11
1
L
Udx
dUF
12
2
With the battery connected, since x is increasing downwards, a negative force is upwards, pushing the dielectric away.With the battery disconnected, the force is positive and pointed downwards, pulling in the dielectric.The force is proportional to (κ-1) and inversely to L.To make the argument simple, we have omitted the fact that the field at the end includes the fringe field which depends on distance between the plates. The result including fringe fields is quantitatively different. See S. Margulies, American Journal of Physics, V. 52, p 515 (1984)
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A questionWhat is the equivalent capacitance between the points A and B?
A. 1 μFB. 2 μFC. 4 μFD. 10μFE. None of these
A B
What would a 10V battery do, i.e. how much charge will it provide, when it is connected across A and B? 40 μC (20 μC) on 2 μF
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HITT
A parallel-plate capacitor has a plate area of 0.2m2 and a plate separation of 0.1 mm. To obtain an electric field of 2.0 x 106 V/m between the plates, the magnitude of the charge on each plate should be:A. 8.9 x 10-7 C B. 1.8 x 10-6 C C. 3.5 x 10-6 C D. 7.1 x 10-6 C E. 1.4 x 10-5 C
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In general a capacitor system
may consist of smaller capacitor
groups that can be identified as
connected "in parallel" or
"in series"
More complex capacitor systems
12 1 2
1 2
12 3
In the example of the figure and in fig.a are connected .
They can be substituted by the equivalent capacitor as
shown in fig.b. Cap
in parallel
acitors and in fig.b are c
C C C
C C
C C
123
123123 12 3
onnected .
They can be substituted by a single capacitor as shown in fig.c
is given by the equation:
in series
1 1
1
C
CC C C
(25 - 12)
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All C’s are 8.00 nF. The battery is 12 V.What is the equivalent capacitance?
C12 = 4 nFC123 = 12 nFQ123 = C123 x V = 144 nCQ3 = C3 x V = 96 nCQ12 = C12 x V = 48 nC
U123 = ½ C123V2 = ½ x 12x10-9 x122 = 864 nJU1 = ½ C1V1
2 = ½ x 8x10-9 x62 = 144 nJ = U2
U3 = ½ x 8x10-9 x122 = 576 nF
C3 stores most energy, also the highest electric field and most charge, the most stressed part of the circuit.
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• Series combinations reduce the capacitance. Equal C reduce by the number involved.
• In parallel the capacitance increases.A basket of 4 capacitors, each of C = 6 nF. How
can you arrange them to get a) 1.5 nFb) 2 nF g) 2.4 nFc) 3 nF h) 3.6 nFd) 4 nF i) 4.5 nF j) 6 nFe) 12 nF k) 18 nFf) 24 nF
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clicker
All C’s are 8.00 nF. The battery is 12 V.What is the equivalent capacitance?
a. 4 nFb. 6 nFc. 8 nFd. 10 nFe. 12 nF
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Circuits
• All capacitors being the same, rank the equivalent capacitances of the four circuits.
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summary
• Capacitance• Parallel plates, coaxial
cables, Earth• Series and parallel
combinations• Energy in a capacitor• Dielectrics• Dielectric strength
CVQ
abaab
abC
abL
dAC
oo
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o
44
)/ln(/2
/
.....111
2121
CCCCCC
C
QCVU
22
1 22
CC
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A question
• Each of the four capacitors shown is 500 μF. The voltmeter reads 1000V. The magnitude of the charge, in coulombs, on each capacitor plate is:
A. 0.2 B. 0.5 C. 20 D. 50 E. none of these