Capacitance

Chapter 18 – Part II

C

Two parallel flat platesthat store CHARGE is called a capacitor.

The plates have dimensions >>d, the plateseparation.

The electric field in aparallel plate capacitoris normal to the plates.

The “fringing fields”can be neglected.

Actually ANY physicalobject that can store chargeis a capacitor.

A Capacitor Stores

CHARGE

V

Apply a Potential Difference V

And a charge Q is found on theplates

CVQV

Q

PotentialC

chargeQ

Unit of Capacitance = F

nFnanofarad

mFmillifarad

Fmicrofarad

Farad11

C

Volt

Thin Film Structure

Variable Capacitor and 1940’s Radio

One Way to Charge:

Start with two isolated uncharged plates. Take electrons and move them from the + to

the – plate through the region between. As the charge builds up, an electric field

forms between the plates. You therefore have to do work against the

field as you continue to move charge from one plate to another.

The two metal objects in the figure have net charges of +79 pC and -79 pC, which result in a 10 V potential difference between them.

(a) What is the capacitance of the system? [7.9] pF(b) If the charges are changed to +222 pC and -222 pC, what does the capacitance become? [7.9] pF(c) What does the potential difference become?[28.1] V

TWO Types of Connections

SERIES

PARALLEL

Parallel Connection

VCEquivalent=CE

321

321

321

33

22

1111

)(

CCCC

therefore

CCCVQ

qqqQ

VCq

VCq

VCVCq

E

E

E

Series Connection

V C1 C2

q -q q -q

The charge on eachcapacitor is the same !

Series Connection Continued

21

21

21

111

CCC

or

C

q

C

q

C

q

VVV

V C1 C2

q -q q -q

More General

ii

i i

CC

Parallel

CC

Series

11

Example

C1 C2

V

C3

C1=12.0 fC2= 5.3 fC3= 4.5 d

(12+5.3)pf

series

(12+5.3)pf

A Thunker

Find the equivalent capacitance between points a and b in the combination of capacitors shown in the figure.

V(ab) same across each

d

A

d

A

Ed

A

V

A

V

A

V

QC 0

0

d

VE :Remember

A capacitor is charged by being connected to a battery and is then disconnected from the battery. The plates are then pulled apart a little. How does each of the following quantities change as all this goes on? (a) the electric field between the plates, (b) the charge on the plates, (c) the potential difference across the plates, (d) the total energy stored in the capacitor.

Stored Energy

Charge the Capacitor by moving q charge from + to – side.

Work = q Ed=q(V/d)d=qV

W=qV=Sum of strips

0V

0Qq

V

20

00

00

2

1

2

1

CVW

CVQ

VQqVW

20

20

20

2202

2

1

)(2

1

2

1

2

1

2

1

EVol

WityEnergyDens

VolEdAEW

dEd

ACVW

Energy Density

DIELECTRIC

Stick a new material between the plates.

We can measure the C of a capacitor (later)

C0 = Vacuum or air Value

C = With dielectric in place

C=C0 0

0

V

VV

C

CK

Dielectric Breakdown!

Messing with Capacitors

+

V-

+

V-

+

-

+

-

The battery means that thepotential difference acrossthe capacitor remains constant.

For this case, we insert the dielectric but hold the voltage constant,

q=CV

since C C0

qC0V

THE EXTRA CHARGE COMES FROM THE BATTERY!

Remember – We hold V constant with the battery.

Another Case We charge the capacitor to a voltage V0.

We disconnect the battery. We slip a dielectric in between the two plates. We look at the voltage across the capacitor to

see what happens.

No Battery

+

-

+

-

q0

q

q0 =C0Vo

When the dielectric is inserted, no chargeis added so the charge must be the same.

0

0000

0

VV

or

VCqVCq

VCq

V0

V

Another Way to Think About This

There is an original charge q on the capacitor.

If you slide the dielectric into the capacitor, you are adding no additional STORED charge. Just moving some charge around in the dielectric material.

If you short the capacitors with your fingers, only the original charge on the capacitor can burn your fingers to a crisp!

The charge in q=CV must therefore be the free charge on the metal plates of the capacitor.

A little sheet from the past..

+++

---q-q

-q’ +q’

A

q

A

qE

A

qE

dialectricsheet

sheet

00/

00

'

2

'2

2

'

2

0 2xEsheet 0

Some more sheet…

A

qqE

so

A

qE

A

qE echdielectric

0

00

0arg

'

'