# Capacitors - PowerPoint PPT Presentation

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Capacitors. A device storing electrical energy. – – – – – – –. + + + + + + +. –q. +q. Capacitor. A potential across connected plates causes charge migration until equilibrium. Charge stored q = C D V C = capacitance Unit = C/V = henry = H. D V. A. C 2. N m 2.

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Capacitors

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## Capacitors

A device storing electrical energy

– –

– –

– –

+ +

+ +

+ +

+

–q

+q

### Capacitor

A potential across connected plates causes charge migration until equilibrium

Charge stored

q = CDV

C = capacitance

Unit = C/V = henry = H

DV

A

C2

N m2

e0 = 8.8510–13

### Parallel Plate Capacitance

Plate area A, separation d

d

Capacitance = Ae0/d

+ –

DV

• Conductor

• Capacitor

or

• Resistor

### Circuit Element Symbols

• Potential Source

DV

+ –

C

+ –

DV

### At Equilibrium

• Capacitor charges to potential DV

• Capacitor charge Q = CDV

DQ

slope = 1/C

DV

area = W

Q

### Energy in a Capacitor

• C = Q/DV so DV = Q/C

• Work to push charge DQ W =DVDQ = (Q/C)DQ

DV

Q/C

Q

### Energy in a Capacitor

• Work to charge to Q is area of triangleW = 1/2 Q(Q/C) = 1/2 Q2/C

• Work to charge to DVW = 1/2 DV (CDV) = 1/2C(DV)2

CDV

Series

Parallel

and

### Parallel Components

• All have the same potential difference

• Capacitances add

• (conceptually add A’s)

### Series Capacitors

• All have the same charge separation

• Reciprocals are additive

• (conceptually add d’s)

• e0 = 8.8510–13

C2

N m2

### Gauss’s Law

• Electric flux through a closed shell is proportional to the charge it encloses.

FE = Qin/e0

R

q

q

1

q

kq

e04pr2

if k =

=

=

e0A

4pe0

4pe0 r2

r2

### Field around a Point Charge

Shell Area = 4pr2

FE = q/e0 = EA

+q

E =

=

s

1

sA

FE =

, so E =

e0

2

e0

### Field Around Infinite Plate

With uniform charge density s = Q/A

= E(2A)

–q

–q

+q

1/2 s/e0

0

0

+q

s/e0

1/2 s/e0

### Infinite ||-Plate capacitor

Individually

Together

• Field E =

=

s

Q

e0

Ae0

Qd

• Potential DV = Ed =

Ae0

Q Ae0

Ae0

• Capacitance Q/DV =

=

Qd

d

### Parallel Plate Capacitance

• Plate area A, plate separation d