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Electrostatic Energy and Capacitors - General Physcis - Lecture Slides, Slides of Physics

Physics is about nature. This course covers almost every concept related to physics. Important points in this lecture are: Electrostatic Energy and Capacitors, Electrostatic Energy, Capacitors, Using Capacitors, Energy in the Electric Field, Lifesaving Jolt, Defibrillator, Work Done, Configuration of a System, Charge Transfer

Typology: Slides

2012/2013

Uploaded on 07/12/2013

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23. Electrostatic Energy & Capacitors
1. Electrostatic Energy
2. Capacitors
3. Using Capacitors
4. Energy in the Electric Field
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23. Electrostatic Energy & Capacitors

Electrostatic Energy

Capacitors

Using Capacitors

Energy in the Electric Field

The lifesaving jolt of a defibrillator requires a largeamount of energy delivered in a short time.Where does that energy come from?

Capacitor

Capacitors

Capacitor: pair of conductors carrying equal but opposite charges.

Usage: store electrical energy

Parallel-Plate Capacitor:2 conducting plates of area

A

separated by a

small distance

d

.

Plates are initially neutral.They’re charged by connecting to a battery.Charge transfer

plates are equal but oppositely charged.

Large

A

, small

d

E

0 outside.

0

inside

E

z

Far from the edges

0

Q
A

z

^

 ˆ

inside

V

d

E

z

Q 0

d A

Capacitance

Q 0
V

d A

Parallel-plate capacitor:

0

A
Q
V

d

C V

0

A
C

d   C = Q

/

V

= capacitance

Parallel-plate capacitorSee Probs 41 & 42

^

^

C
C
V

farad

F

Practical capacitor ~

F ( 10

^6

F) or pF ( 10

^12

F )

^

 0

C d

A

^
F

m

dV

dQ C

Charging / Discharging

dQ

C

dV

Example 23.1. Parallel-Plate Capacitor

A capacitor consists of two circular metal plates of radius

R

= 12 cm,

separated by

d

= 5.0 mm. Find

(a) Its capacitance,(b) the charge on the plates, and(c) the stored energy when the capacitor is connected to a 12-V battery.

0

A
C

d

 

10

F

^

2

9

3

/^

m

Vm

C

m

 

pF

(a) (b) (c)

Q
C V

^

^

^

pF

V

pC

2

U
C V

^

^

^

pF

V

pJ

nJ

C
F
V

Using Capacitors

Computer memories: billions of 25 fF capacitors.Rectifiers: mFFuel-cells: 10

2

F

220-mFelectrolyticcapacitor

1 F

43 pF to 2.2 mF

Dielectrics

Dielectrics: insulators containing molecular dipoles but no free charges.

Dielectric layer lowers V betweencapacitor plates by factor 1/

(

1).

0

A d

Q
C
V

= dielectric constant

Molecular dipolesaligned by

E

0

.

Dipole fields oppose

E

. 0

Net field reduced to

E

=

E

0

/

.

Hence

V

=

V

0

/

.

Q

is unchanged, so

C

=

C

0

.

: 2 ~ 10 mostly

Working voltage V = Max safe potential < E

bkd

d

GOT IT? 23.1.

You need to replace a capacitor with one that can store more energy.Which will give you greater energy increase:(a) a capacitor with twice the capacitance and same working voltage as the old one,or (b) a capacitor with the same capacitance and twice the working voltage?

Connecting Capacitors

Two ways to connect 2 electronic components: parallel & series

Parallel:

Same

V

for both components

Q
C V

1

2

Q
Q

1

2

C V
C V

1

2

C
C
C

Series:

Same

I

(

Q

) for both components

Q
V
C

1

2

V
V

1

2

Q
Q
C
C

1

2

C
C
C

1

2

C
C

or C

1

2

C
C

or C

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Making the Connection

You’ve got two 10-

F capacitors rated at 15 V.

What are the capacitances & working voltages of their parallel & series combinations?Parallel :

C
F
F

working V

V

Series :

C
F
F

working V

V
V

1

2

V
V
V

1

2

V
V
V

GOT IT? 23.2.

You have 2 identical capacitors with capacitance

C

.

How would you connect them to get equivalent capacitances(a) 2

C

, and

(b) ½ C ?Which combination would have the higher working voltage?

parallel

series

Bursts of Power

San Francisco’s BART train:KE of deceleration stored as EE in ultracapacitor.Stored EE is used to accelerate train.

Capacitors deliver higher energymuch more quickly than batteries.Flash light:Battery charges capacitor,which then discharges to give flash.

Other examples:Defibrillator, controlled nuclear fusion, amusement park rides, hybrid cars, …

23.4. Energy in the Electric Field

Charging a capacitor rearranges charges

energy stored in

E

Energy density = energy per unit volume

Parallel-plate capacitor:

2 Q 2

U
C

(^20)

2

Q

A d

E

U

u

A d

Energy density :

2

2

0 2

Q
A

2 0

2

0

1 2

E

0

E

is universal

2

0

1 2

E u

E

^

^

3

/

E u

J

m

2

0 1 2

U

dV

E