CAPACITORS

68
September 29, 2008 CAPACITORS

description

CAPACITORS. September 29, 2008. How did you do?. Great OK Poor Really bad I absolutely flunked!. Calendar of the Day. Exams will be returned within a week. If you did badly in the exam you need to have a plan to succeed. Let me know if you want any help with this. - PowerPoint PPT Presentation

Transcript of CAPACITORS

Page 1: CAPACITORS

September 29, 2008

CAPACITORS

Page 2: CAPACITORS

How did you do?

A. GreatB. OKC. PoorD. Really badE. I absolutely

flunked!

Page 3: CAPACITORS

Calendar of the DayCalendar of the DayExams will be returned within a week.

If you did badly in the exam you need to have a plan to succeed. Let me know if you want any help with this.

Quiz on Friday – Potential or Capacitance.WebAssign will appear shortly if it hasn’t

done so already.There is a WA on board for potential.Quizzes are in the bin on the third floor

through the double doors.

Page 4: CAPACITORS

Two +q charges are separated by a distance d. What is the potential at a point midway between the charges on the line connecting them

A. ZeroB. Kq/dC. Kq/dD. 2Kq/dE. 4kq/d

Page 5: CAPACITORS

Capacitors

Page 6: CAPACITORS

A simple Capacitor

Remove the battery Charge Remains on the

plates. The battery did WORK to

charge the plates That work can be

recovered in the form of electrical energy – Potential Difference

WIRES

TWO PLATES

Battery

WIRES

Page 7: CAPACITORS

INSIDE THE DEVICE

Page 8: CAPACITORS

Two Charged Plates(Neglect Fringing Fields)

d

Air or Vacuum

Area A

- Q +QE

V=Potential Difference

Symbol

ADDED CHARGE

Page 9: CAPACITORS

Where is the charge?d

Air or Vacuum

Area A

- Q +QE

V=Potential Difference

------

++++++

AREA=A

=Q/A

Page 10: CAPACITORS

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.

Page 11: CAPACITORS

Capacitor

Page 12: CAPACITORS

More on Capacitors

000

0

0

0

)/(

0

AQA

QE

EAQ

QEAAEA

qd

Gauss

AE

d

Air or Vacuum

Area A

- Q +QE

V=Potential Difference

GaussianSurface

Same result from other plate!

Page 13: CAPACITORS

DEFINITION - CapacityThe Potential Difference is

APPLIED by a battery or a circuit.

The charge q on the capacitor is found to be proportional to the applied voltage.

The proportionality constant is C and is referred to as the CAPACITANCE of the device.

CVqor

VqC

Page 14: CAPACITORS

UNITSUNITSA capacitor which

acquires a charge of 1 coulomb on each plate with the application of one volt is defined to have a capacitance of 1 FARAD

One Farad is one Coulomb/Volt

CVqor

VqC

Page 15: CAPACITORS

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

Page 16: CAPACITORS

NOTEWork to move a charge from one side of a capacitor to the other is qEd.

Work to move a charge from one side of a capacitor to the other is qV

Thus qV=qEdE=V/d As before

Page 17: CAPACITORS

Continuing…

dAC

sodAVEAAq

VqC

0

00

The capacitance of a

parallel plate capacitor depends only on the Area and separation between the plates.

C is dependent only on the geometry of the device!

Page 18: CAPACITORS

Units of Units of 00

mpFmF

andm

FaradVoltm

CoulombVoltCoulombm

CoulombJoulem

CoulombNm

Coulomb

/85.8/1085.8 120

2

2

2

2

0

Page 19: CAPACITORS

Simple Capacitor CircuitsBatteries

Apply potential differencesCapacitorsWires

Wires are METALS.Continuous strands of wire are all at the same

potential.Separate strands of wire connected to circuit

elements may be at DIFFERENT potentials.

Page 20: CAPACITORS

Size Matters!A Random Access Memory stores

information on small capacitors which are either charged (bit=1) or uncharged (bit=0).

Voltage across one of these capacitors ie either zero or the power source voltage (5.3 volts in this example).

Typical capacitance is 55 fF (femto=10-15)Probably less these days!

Question: How many electrons are stored on one of these capacitors in the +1 state?

Page 21: CAPACITORS

Small is better in the IC world!

electronsC

VFe

CVeqn 6

19

15

108.1106.1

)3.5)(1055(

Page 22: CAPACITORS

October 1, 2008

Cap-II

Page 23: CAPACITORS

Note:I do not have the grades yet. Probably by

Friday.Quiz on Friday … Potential or Capacitors.Watch WebAssign for new stuff.

Page 24: CAPACITORS

Last TimeWe defined

capacitance:C=q/VQ=CV

We showed thatC=0A/d

AndE=V/d

Page 25: CAPACITORS

TWO Types of Connections

SERIES

PARALLEL

Page 26: CAPACITORS

Parallel Connection

VCEquivalent=CE

321

321

321

33

22

1111

)(

CCCCtherefore

CCCVQqqqQ

VCqVCq

VCVCq

E

E

E

Page 27: CAPACITORS

Series Connection

V C1 C2

q -q q -q

The charge on eachcapacitor is the same !

Page 28: CAPACITORS

Series Connection Continued

21

21

21

111CCC

orCq

Cq

Cq

VVV

V C1 C2

q -q q -q

Page 29: CAPACITORS

More GeneralMore General

ii

i i

CC

ParallelCC

Series11

Page 30: CAPACITORS

Example

C1 C2

V

C3

C1=12.0 fC2= 5.3 fC3= 4.5 d

(12+5.3)pf

series

(12+5.3)pf

Page 31: CAPACITORS

More on the Big CWe move a charge

dq from the (-) plate to the (+) one.

The (-) plate becomes more (-)

The (+) plate becomes more (+).

dW=Fd=dq x E x d+q -q

E=0A/d

+dq

Page 32: CAPACITORS

So….

2222

0

2

0

2

0 0

0

00

21

22

)(

122

1

1

CVCVC

CQU

ordA

qAdqqdq

AdUW

dqdAqdW

AqE

GaussEddqdW

Q

Page 33: CAPACITORS

Not All Capacitors are Created Equal

Parallel Plate

CylindricalSpherical

Page 34: CAPACITORS

Spherical Capacitor

???4

)(

4

02

0

2

0

surpriserqrE

qEr

qd

Gauss

AE

Page 35: CAPACITORS

Calculate Potential Difference V

drr

qV

EdsV

a

b

platepositive

platenegative

20

.

.

14

(-) sign because E and ds are in OPPOSITE directions.

Page 36: CAPACITORS

Continuing…

abab

VqC

ababq

baqV

rq

rdrqV

b

a

0

00

02

0

4

411

4

)1(44

Lost (-) sign due to switch of limits.

Page 37: CAPACITORS

A Thunker

If a drop of liquid has capacitance 1.00 pF, what is its radius?

STEPS

Assume a charge on the drop.Calculate the potentialSee what happens

Page 38: CAPACITORS

In the drawing below, find the equivalent capacitance of the combination. Assume that C1 = 8 µF, C2 = 4 µF, and C3 = 3  µF.

5.67µF

Page 39: CAPACITORS

In the diagram, the battery has a potential difference of 10 V and the five capacitors each have a capacitance of 20 µF.

What is the charge on( a) capacitor C1 and (b) capacitor C2?

Page 40: CAPACITORS

In the figure, capacitors C1 = 0.8 µF and C2 = 2.8 µF are each charged to a potential difference of V = 104 V, but with opposite polarity as shown. Switches S1 and S2 are then closed.

(a) What is the new potential difference between points a and b? 57.8 VWhat are the new charges on each capacitor?(b)46.2µC (on C1)(c)162µC (on C2)

Page 41: CAPACITORS

Anudder ThunkerAnudder ThunkerFind the equivalent capacitance between points a and b in the combination of capacitors shown in the figure.

V(ab) same across each

Page 42: CAPACITORS

DIELECTRIC

Page 43: CAPACITORS

Polar Materials (Water)

Page 44: CAPACITORS

Apply an Electric Field

Some LOCAL ordering Larger Scale Ordering

Page 45: CAPACITORS

Adding things up..

- +Net effect REDUCES the field

Page 46: CAPACITORS

Non-Polar Material

Page 47: CAPACITORS

Non-Polar Material

Effective Charge isREDUCED

Page 48: CAPACITORS

We can measure the C of a capacitor (later)

C0 = Vacuum or air Value

C = With dielectric in place

C=C0

(we show this later)

Page 49: CAPACITORS

How to Check This

Charge to V0 and then disconnect fromThe battery.C0 V0

Connect the two togetherV

C0 will lose some charge to the capacitor with the dielectric.We can measure V with a voltmeter (later).

Page 50: CAPACITORS

Checking the idea..

00

0

000

210

2

01

000

1 CVVCC

CVVCVCqqq

CVqVCqVCq

V

Note: When two Capacitors are the same (No dielectric), then V=V0/2.

Page 51: CAPACITORS
Page 52: CAPACITORS

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.

Page 53: CAPACITORS

Another CaseWe 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.

Page 54: CAPACITORS

No Battery

0

0000

0

VV

orVCqVCq

VCq

+

-

+

-

q0

q

q0 =C0Vo

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

V0

V

Page 55: CAPACITORS

Another Way to Think About ThisThere 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.

Page 56: CAPACITORS

A Closer Look at this stuff..

00

00

00

VdAVCq

dAC

Consider this virgin capacitor.No dielectric experience.Applied Voltage via a battery.

C0

++++++++++++

------------------

V0

q

-q

Page 57: CAPACITORS

Remove the Battery

++++++++++++

------------------

V0

q

-q

The Voltage across thecapacitor remains V0

q remains the same aswell.

The capacitor is fat (charged),dumb and happy.

Page 58: CAPACITORS

Slip in a DielectricAlmost, but not quite, filling the space

000

0

....

AqE

qd

gapsmallin

AE

++++++++++++

------------------

V0

q

-q

- - - - - - - -

+ + + + + +

-q’

+q’

E0

E

E’ from inducedcharges

Gaussian Surface

Page 59: CAPACITORS

A little sheet from the past..

Aq

AqE

AqE

dialectricsheet

sheet

00/

00

'2

'2

2'

2

+++

---q-q

-q’ +q’

0 2xEsheet 0

Page 60: CAPACITORS

Some more sheet…

AqqE

soAqE

AqE echdielectric

0

00

0arg

'

'

Page 61: CAPACITORS

A Few slides backNo Battery

+

-

+

-

q0

q

q=C0Vo

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

0

0000

0

VV

orVCqVCq

VCq

V0

V

Page 62: CAPACITORS

From this last equation

0

00

00

0

1

EE

EE

VVthus

dEVEdV

and

VV

Page 63: CAPACITORS

Another look

dV

AQdVE

FieldElectricdAVVCQ

dAC

PlateParallel

0000

00

00000

00

+

-

Vo

Page 64: CAPACITORS

Add Dielectric to CapacitorOriginal Structure

Disconnect Battery

Slip in Dielectric

+

-

Vo

+

-

+

-

V0

Note: Charge on plate does not change!

Page 65: CAPACITORS

What happens?

0

00 1

VEdV

anddVEE

00 /

CVQ

VQC

+

-

ii

oo

Potential Difference is REDUCEDby insertion of dielectric.

Charge on plate is Unchanged!

Capacitance increases by a factor of as we showed previously

Page 66: CAPACITORS

SUMMARY OF RESULTS

0

0

0

EE

CC

VV

Page 67: CAPACITORS

APPLICATION OF GAUSS’ LAW

qqq

andA

qE

EAqqE

AqE

'

'

0

0

0

00

Page 68: CAPACITORS

New Gauss for Dielectrics

0

0

sometimes

qd freeAE