C 0 A

d

C Q

V

Capacitors: Store Electric Energy

To calculate:

1) Put on arbitrary ±Q

2) Calculate E

3) Calculate V

Parallel Plate Capacitor:

P8-

Batteries & Elementary Circuits

P8- 2

Ideal Battery

Fixes potential difference between its terminals

Sources as much charge as necessary to do so

Think: Makes a mountain

P8- 3

Batteries in Series

V1

P8- 4

V2

Net voltage change is V = V1 + V2

Think: Two Mountains Stacked

Batteries in Parallel

Net voltage still VDon’t do this!

P8- 5

Capacitors in Parallel

P8- 6

Capacitors in Parallel

Same potential!

C Q1 , C Q2

1 V 2

V

P8- 7

Equivalent Capacitance

?

Q Q1 Q2 C1V C2V

C1 C2 V

C Q C C1 2eq V

P8- 8

Capacitors in Series

Different Voltages Now

What about Q?

P8- 9

Capacitors in Series

P8- 10

Equivalent Capacitance

1 2C1 C2V Q , V Q

V V1 V2

(voltage adds in series)

V = Q Q QC1 C2Ceq

C1 C2

1 1 1 Ceq

P8- 11

PRS Question: Capacitors in Series and Parallel

When capacitors are combined, they behave in an opposite way comparing to resistors.

P8- 13

Dielectrics

P8- 14

A dielectric is a non-conductor or insulator

Examples: rubber, glass, waxed paper

When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates

HOW???

Molecular View of Dielectrics

Polar Dielectrics :

Dielectrics with permanent electric dipole moments

Example: Water

P8- 15

Molecular View of Dielectrics

Non-Polar Dielectrics

Dielectrics with induced electric dipole moments

Example: CH4

P8- 16

Dielectric in Capacitor

Potential difference decreases because dielectric polarization decreases Electric Field!

P8- 17

Gauss’s Law for Dielectrics

Upon inserting dielectric, a charge density ’ is induced at its surface

0 0 S

insideqE dA EA

E '

0

' A

P8- 18

What is ’?

Dielectric Constant Dielectric weakens original field by a factor

E ' E0

0

0 ' ⎛1 1 ⎞

⎠⎜⎟⎝

P8- 19

Bound charge = free charge (1-1/ )k

Total net charge = free charge – bound charge = free charge/k

' /

Dielectric Constant Dielectric weakens original field by a factor

Very often, people use e instead of k to represent dielectric constant.

Dielectric constants

P8- 20

Vacuum 1.0Paper 3.7

Pyrex Glass 5.6

Water 800

0

AC

d

For a vacuum(air)-filled capacitor

For a dielectric-filled capacitor

?C

=1 k for vacuum. >1 k for other insulators (dielectrics).

Dielectric in a CapacitorQ0= constant after battery is disconnected

Upon inserting a dielectric:

Q0 Q0 C0

0 0

C Q VV /

VP8- 21Dielectric filling will increase C by a factor of , k when free charge

Q is unchanged, E field and DV will reduce by a factor of . k

E and V reducesdue to bounded charges.

Dielectric in a CapacitorV0 = constant when battery remains connected

Upon inserting a dielectric: Q Q0

C Q C Q0

P8- 22

0V0V

Dielectric filling increases C by a factor of ,kWhen DV is constant, Q increase by a factor of .k

PRS Questions: Dielectric in a Capacitor

P8- 23

Capacitors & DielectricsTo calculate:

1) Put on arbitrary ±Q

2) Calculate E

3) Calculate VC Q

VEnergy

2

Capacitance

21

2

Q 1

2C 2C V

P10-

Q V U 2

3 3

2o

E

Eu d r d r

Dielectrics

When DV is fixed, adding dielectric filling increases U by a factor of k. When Q (free charge) is unchanged, adding dielectric filling decreases U by a factor of k.

00

AC

d

For a vacuum(air)-filled capacitor

21

2

Q 1

2C 2C V Q V U 3

Eu d r= uEAd2 2

200

1

2 2 2E

C VU Vu E

Ad Ad d

0 AC

d

For a dielectric-filled capacitor

2 220

0

1

2 2 2E

C VU Vu E

Ad Ad d