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

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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

Docsity.com

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