1. Capacitors Q D
A capacitor is a device that is capable of storing electric charges and thus electric potential energy.
=> charging
Its purpose is to release them later in a controlled way.
=> discharging
Capacitors are used in vast majority of electrical and electronic devices. +Q -Q
Typically made of two conductors and, when charged, each holds equal and opposite charges.

2. DOCCAM 2 DEMO 5A-28 PARALLEL PLATE CAPACITOR

3. Polar and Nonpolar Dielectrics
Polar dielectrics: dielectric material whose molecules have permanent electric dipole moments, such as water.
Eext = 0: the orientations of the permanent electric dipoles are distributed randomly, so the net dipole moment of the material is zero.
Eext > 0 : the molecular dipoles try to align themselves with the field against random thermal motion, resulting in a net dipole moment.
Nonpolar dielectrics: molecules with no permanent electric dipole moments.
Eext > 0 : ± charges separate, induced dipole moment emerges.
Show the first demo:5A-31

4. READING QUIZ 1
A capacitor C0 with air dielectric κ =1 is charged to a potential V and then is disconnected from the battery. A uniform dielectric with dielectric constant κ > 1 is inserted into the capacitor and occupies the full volume of the capacitor. If the original electric field is E0 and the final electric field is Eκ , which of the following statements is correct.? A| E0 = Eκ B| E0 < Eκ C| E0 > Eκ D| E0 = Eκ / κ

5. Dielectrics between Capacitor Plates
+ Q
- Q
free charges
Electric field E between plates can be calculated from Q – q.
neutral -q +q
Polarization
Charges ± q
The presence of a dielectric weakens the electric field, therefore weaken the potential drop between the plates, and leads to a large capacitance.

6. DOCCAM 2 DEMO 5A-30 EFFECT OF DIELECTRICS ON CAPACITANCE

7. Inserting Dielectrics (= Insulator)
Inserting a dielectric between the plates of a capacitor increases capacitance
Q=CV
holds more charges at fixed V
Dielectric constant κ of a dielectric is the ratio of the capacitance when filled with it to that without it:
κ > 1 always (dimensionless)
Material κ
air (1 atm)
paper
3.7
pyrex
5.6
water (20 o C)
80.4
strontium titanate
310
Under the same Q,
V = V0/k
E = E0/k
Show demo: 5A-30
Breakdown potential determined by dielectric strength (Emax)

8. Capacitors in Parallel
V is common
Equivalent Capacitor:
where

9. Capacitors in Series
q is common
Equivalent Capacitor:
where

10. Conductor inserted between plates
A parallel-plate capacitor with conductor inserted in the middle
Two capacitors of area A in series +q +q a -q -q -Q -Q +q +q b -q -q
E=0 outside capacitors
E=0 in conductor
between plates
between plates
(a)

11. Warm-up quiz 2
All the capacitors have the same capacitance C, What is the total capacitance between A and B? A B
A). 4/3 C
B). 3/4 C
C). 3/2 C
D). 1/2 C
E). 2/3

12. Non-uniform Parallel-plate Capacitor 1
Equivalent to 2 capacitors in parallel
Potential drop V in each is the same.
Note a if
even though

13. Non-uniform Parallel-plate Capacitor 2
Equivalent to 2 capacitors in series
(Free) charge in each Q is the same. a
Note if

14. Inserting Dielectric Material with Battery Disconnected
Charge a parallel plate capacitor filled with air (or vacuum) to potential difference V0.
Deposits charge Q
2. Disconnect the battery
Q remains fixed -Q
3. Insert a dielectric of dielectric constant κ Q
So, V and E decreases from V0 , E0 to
and -Q
and

15. Energy stored in a capacitor revisited+Q -Q
Battery disconnected
Separation ~ 0 +Q -Q
Change in separation Δ d
External work required to separate the plates from zero to d m apart is
What if a battery remains connected?

16. Inserting Dielectric Material with Battery Connected
Charge a parallel plate capacitor filled with vacuum (air) to potential difference V.
Deposits charge
2. Keep the battery connected
V remains fixed
3. Insert a dielectric of dielectric constant κ
So, Q increases from Q0 and E remains fixed
and
and

17. Force and energy with battery connected, a mystery?
Force between plates? +Q -Q
Battery connected V
attractive
Work to change separation from 0 to d?
Separation ~ 0 +Q -Q
Q changes
Separation Δ d
Separation
d+Δd
Separation d
However,
Why? Battery must be included in energy conservation !

18. Lecture 10:30 quiz 3 September 20, 2011
Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the capacitance from A to B? a b e A B c d
A). 2C
B). 1/(1+k) C
C). (1+k)C
D). 5 C
E). [4/(4+k)] C

19. Lecture 11:30 quiz 3 September 22, 2011
Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the total capacitance from A to B? a b e A B c d
A). 2C
B). [k/(1+k)] C
C). (1+k)C
D). [1/(1+k)] C C
E). (4+k) C

20. Lecture 11:30 quiz 3, February 8, 2011
Four identical capacitors have the same capacitance C. Then capacitor (a) is filled with a material with dielectric constant k. What is the total capacitance from A to B? a b A B c d
A). (3/2 + k) C
B). (3+k) C
C). 5/2 C
D). (2/3 +k) C
E). (3+k) C