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PHYS142

CH 26Materials for Lecture

Poling cards

Demos: http://www.physics.umd.edu/deptinfo/facilities/lecdem/lecdem.htm

J4-01

J4-22

J4-51

Animations courtesy of:http://webphysics.davidson.edu/Applets/Applets.html

T E S T I N G

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PHYS142

CH 26Capacitors

Fields near point charges is all well and good, but let’s do something practical!

Capacitors are found in all electric circuits.

Capacitor Industries, IncChicago, IL

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PHYS142

CH 26Capacitors

A capacitor is a way of storing charge. The symbol for a capacitor in a schematic for an electrical circuit shows basically what it is: two plates with a gap.

The charges are held together on the plates by their attraction.

(often want to store charge so that it can provide current)

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PHYS142

CH 26Storing ChargeLet’s think about storing charge…Often, you want to store as much charge as possible, while avoiding large (dangerous) voltages

0 0

0

V Ed

QE

A

VAQ

d

For a fixed voltage, you can increase the charged stored by increasing A or decreasing d

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PHYS142

CH 26Capacitance

0 0VA AQQ

d V d

Or the charge you can store per volt is related to the geometry of the plates and the gap

Capacitance is the amount of charge you can store per volt, or Q/V.

Farad=coulomb/volt

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CH 26Increasing Area

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CH 26Test Yourself

I’m going to charge these plates to 1000 V. I’m going to remove the charger, then I’m going to move them apart. As I move them, will the voltage

1) Increase2) Decrease3) Stay the same

Demo j4-01

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CH 26ExampleWhat would be the area of a capacitor with a gap of ½ mm to have a capacitance of 1 farad?

0

12

6 2

8.85 10 10.0005

56 10

AC

dA

x

A x m

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PHYS142

CH 26Example

Air breaks down and conducts for an electric field strength of 3x106 V/m. How many volts can it hold if it has a gap of 1mm?

63 10 0.001 3000V Ed x V

Capacitors come with voltage ratings. Cheap capacitors can typically hold 50 V.

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PHYS142

CH 26The Gap

What if I stick something inside the gap?

Maybe something made of molecules that are electric dipoles… • ceramics• mica• polyvinyl chloride• polystyrene• glass• porcelain• rubber• electrolyte (glyco-ammonium borate, glycerol-ammonium borate, ammonium lactates, etc dissolved in goo or paste)

Dielectric material

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CH 26Inside: Dipoles

Electric Dipole moments in random directions

Put a charge on the plates. The charge creates an electric field. Dipole moments try to align with the field.

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CH 26Capacitors

1

2 3

45

6

7 8 9 1011

12

1) 365 pf, 200V, air variable

2) 0.25 F, 3000V, mineral oil

3) 21000 F, 25 V, electrolytic

4) 20 pF, 100 V, air variable

5) 2 F, 400 V, polystyrene

6) 100 F, 12 V, electrolytic

7) 10 pf, 200 V, glass/air

8) 0.1 F, 10 V, ceramic

9) 0.1 F, 1 kV, ceramic

10) 0.33 F, 400 V, mylar

11) 100 pF, 2kV, ceramic

12) 1000 pF, 200V, silver mica

1) Tune radios, 2) filter HV, 3) power supply filter, 4) tune rf, 5) audio 6) audio, 7) vhf/uhf, 8) audio, 9) audio, 10) audio, 11) high power rf, 12) precision rf

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PHYS142

CH 26Test Yourself

Will the field between (and thus the voltage between) the plates be

1) Larger

2) Smaller

3) The same

As without the dielectric?

Do j4-22

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CH 26Inside: Fields

The field goes down. So, the amount of charge you can put on for 1 volt is larger. So, the capacitance goes up.

A certain fraction of the field is “canceled”. E=E0/V=V0/. C=C0

0

0

A AC

d d

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PHYS142

CH 26Dielectrics

Material Breakdown field (106 V/m)---------------------------------------------------------------Air 1.00059 3Paper 3.7 16Glass 4-6 9Paraffin 2.3 11Rubber 2-3.5 30Mica 6 150Water 80 0

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PHYS142

CH 26Example

What area would a capacitor with a 0.5 mm gap have to for a capacitance of 1 farad if it had a dielectric constant () of 10?

Found earlier that without dielectric, need an area of 56x106 m2. So, reduce this by 10 to 56x105 m2

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PHYS142

CH 26Example

A typical capacitor has a capacitance of 10 F, a gap of 0.1 mm, and is filled with a dielectric with a dielectric strength of 10. What is the area?

620

120

Cd 10 10 0.0001; A= 11

10 8.85 10

A xC m

d x

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PHYS142

CH 26Energy Stored

How much work to move some this charge onto the capacitor?

Amount of work to charge from scratch. Sum (integral) up the contributions to bring each charge

QW qV q

C

2

0

1

2

QQ Q

W dQC C

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CH 26Energy Stored

But, Q is hard to measure

2 2 221 1 1

2 2 2

Q C VW CV

C C

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CH 26Simple Circuits

Let’s try our first simple circuit

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CH 26Capacitors with a Battery

An “ideal” battery is a source of constant voltage. Though it is done using properties of metal, ions, etc, you should think of it as containing a fixed E field.

Charge on one side is at a higher potential than the other

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PHYS142

CH 26Batteries

Students have many misconceptions about batteries, which lead to serious difficulties in making predictions about circuits.

Batteries are not charged. They do not contain a bunch of electrons, ready to “spit out”

Batteries are not current sources. They don’t put out a constant current.

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CH 26Ground

Zero volt point. Reservoir of electrons. Can take and give electrons easily.

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CH 26Circuits

Remember: it takes no work to move an charge through a conductor. The potential does not change! (for an ideal conductor… since only a “superconductor” is an ideal conductor, this is only mostly true for copper, gold, etc)

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PHYS142

CH 26Test Yourself

When I close the switch will the voltage across the battery

1) Go down because charge leaves the battery to go to the capacitor

2) Go up because the battery will get additional charge from the capacitor

3) Stay the same because the voltage across a battery always stays the same

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CH 26Battery + Capacitor

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CH 26Example

What is the charge on a 1 F capacitor attached to a 1.5 V battery?

-6 Q=CV=1x10 1.5 1.5Q

C FV

How many electrons is that?

613

19

1.5 1010

1.6 10

xn

x

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PHYS142

CH 26Capacitor Circuits

If you have more than 1 capacitor in a circuit, two basic ways to arrange them

• parallel

• series

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CH 26Parallel Circuits

Connected in Parallel

How will the voltage across them compare?

1) It will half. The voltage from the battery will be divided between the two

2) It will double. Because there will be two capacitors charged

3) It will be the same. The voltage is always the same.

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CH 26Parallel Circuits

How does the charge compare?

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CH 26Parallel

Twice the charge for the same voltage.

Effectively increasing the area of the capacitor

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CH 26Parallel

If you replaced the 2 capacitors with 1 capacitor, what capacitance would it have to have in order to have the same voltage and the same charge -> effective capacitance of the system

1 2effC C C 0AQC

V d

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CH 26Series

How will the voltage across them compare?

1) It will half. The voltage from the battery will be divided between the two

2) It will double. Because there will be two capacitors charged

3) It will be the same. The voltage is always the same.

The voltage across each is 1/2. That means the charge on each is ½ compared to 1 capacitor circuit.

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PHYS142

CH 26Series

Its like you have twice the gap. The effective capacitance goes down.

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CH 26Series in General1 2

1 21 2

1 2

1 2

1 2

1 2

1 2

; V

(1/ 1/ )

1 1 1

eff

V V V

Q QV

C C

Q Q

Q QV

C C

QV

C C

C C C

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PHYS142

CH 26Check

1 2

1 2

1 1 1

1if C

2

eff

eff

C C C

C C C

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PHYS142

CH 26Hints for Capacitors

• remember the voltage across a battery is fixed

• remember voltage does not change along a wire

• look for parallel and series combinations, and calculate the equivalent capacitance.

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PHYS142

CH 26Example

What is the charge on each cap? What is the voltage across each cap?

1) Look for series and parallel combinations. Calculate equivalent capacitance. Replace. Repeat until have 1 cap.

2) Then work backwards1 1 1

1.2 2 3

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PHYS142

CH 26Example

6 62.2 10 13.2 106

Qx F Q x C

V

6

6 6

6

6 6 6

1 10 6 106

1.2 10 7.2 106

6 10 7.2 10 13.2 10

Qx F Q x C

VQ

x F Q x CV

x x x C

6

6

66

7.2 102 10 3.6

7.2 103 10 2.4

3.6 2.4 6

x Cx F V V

V

x Cx F V V

VV

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PHYS142

CH 26ExampleBefore the dielectric is added, the capacitance is C0. What is the capacitance afterwards?

Picture it as two caps in series, each with a gap d/2 and therefore capacitance 2C0.

1 2

1 0 2 0 0 1 2 0 1 2

1 20

1 2

1 1 1 1 1 1( )

2 2 2 2

2

eff

eff

C C C C C

C C

When add dielectric, each capacitance goes up a factor

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PHYS142

CH 26Test Yourself

Which capacitor has the biggest charge?

1) 1F2) 0.2 F3) 0.6F4) They all have the

same charge5) None of the

above

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PHYS142

CH 26Example

What is the equivalent capacitance?

.6 and .2 are in parallel. Add them to get .8

The 1 and the “.8” are in series.

1 1 10.44

1 .8 effeff

C FC

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PHYS142

CH 26Fun

Another use for capacitanceDo j4-51

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PHYS142

CH 26Hints for Capacitor Problems