Lecture 6.2 :!
Capacitors
Lecture Outline:!
Finding Field from Potential!
Capacitance and Capacitors!
Energy Stored in a Capacitor!
Dielectrics!
Textbook Reading:!
Ch. 29.3 - 29.7
Feb. 19, 2015
1
Announcements
!
•HW5 due next Tue. (Feb. 24) at 9am on Mastering Physics.!
•Quiz #3 next Thu. (Feb. 26) in class.
Will cover Ch. 29 material.!
•If you have Satvik Wani as your TA, and you don’t see a grade for
your MidTerm #1 in Blackboard, you need to bring your exam to
either him or me ASAP. Apologies for the hassle.
2
Last Lecture...
f
U=
i
F · ds
V
E=
⇥V
f
V =
i
3
E · ds
Uq+sources
q
Finding Field from Potential
4
Clicker Question #1
Which set of equipotential surfaces
matches this electric field?
Stronger Fields = Closer Equipotentials!
5
Finding Field from Potential
Kirchhoff’s Loop Law
6
Finding Field from Potential
Conductor in Equilibrium
1. Electric Field inside is zero.!
2. Excess charge is on surface.!
3. Surface is equipotential.!
4. Interior is equipotential!
5. Exterior field is
perpendicular to surface.!
6. Field and surface charge
density are largest at sharp
corners. (Why?)
7
Lightning Rods
8
Capacitance and Capacitors
Capacitors come in many shapes/sizes. Common
elements in electrical circuits. “Caps”.
9
Capacitance and Capacitors
Battery charging up a Capacitor
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Capacitance and Capacitors
Q
E=
0A
VC = Ed
Q=
C
C
Capacitance is a
geometric property!
0A
d
VC
Q
VC
Q
0A
=
VC
d
1 farad = 1 F ≡ 1 C/V
11
Clicker Question #2
What is the capacitance of
these two electrodes?
!
A.
B.
C.
D.
E.
8 nF.
4 nF.
2 nF.
1 nF.
Some other value.
12
Capacitance and Capacitors
Capacitors in Series
Capacitors in Parallel
13
Clicker Question #3
Which arrangement has larger equivalent capacitance?
Parallel => add
Series => inverse of sum of inverses
A. Left!
B. Right!
C. Both are equal
14
Energy Stored in a Capacitor
Incremental change in energy
(dU) as charge (dq) is added.
Total Energy Stored
Rewriting in terms of
Potential across Capacitor.
q dq
V =
C
dU = dq
1
UC =
C
Q
0
Q2
q dq =
2C
Q2
1
2
UC =
= C( VC )
2C
2
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Energy Stored in a Capacitor
A 10000 microFarad capacitor is charged to 36V.
What is the energy stored inside this capacitor?!
If the capacitor discharges in 10 microseconds, what is
the power dissipated?
16
Energy Stored in a Capacitor
For a Parallel Plate Capacitor:
1
1 0A
0
2
2
2
UC = C( VC ) =
(Ed) = (Ad)E
2
2 d
2
The energy of a charged capacitor is
stored in the electric field!
17
Dielectrics
So far we’ve assumed our parallel-plate capacitors are
filled with vacuum (i.e. - nothing). What if we insert
some other material?
Capacitance = ?
18
Dielectrics
Capacitor with
no dielectric
Dielectric is
polarized.
19
Electric Field is
diminished.
Dielectrics
VC = Ed =
C=
E0
d=
E0
E
Dielectric
Constant
( V C )0
Voltage
diminishes
Q
Q0
Q0
=
=
= C0
VC
( VC ) 0 /
( V C )0
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Capacitance
Increases
Dielectrics
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Reminders
!
•Show up for recitations!
Make sure you attempt/
study all recitation problems, even if you didn’t get
to them during recitation.!
•HW5 due on Tuesday (Feb. 24) at 9am.!
•Quiz #3 Thursday (Feb. 26)!
!
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