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Capacitors

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Capacitors

A device storing electrical energy

– –

– –

– –

–

+ +

+ +

+ +

+

–q

+q

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 = 8.8510–13

Plate area A, separation d

d

Capacitance = Ae0/d

+ –

DV

- Conductor

- Capacitor

or

- Resistor

- Potential Source

DV

+ –

C

+ –

DV

- Capacitor charges to potential DV
- Capacitor charge Q = CDV

DQ

slope = 1/C

DV

area = W

Q

- C = Q/DV so DV = Q/C

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

DV

Q/C

Q

- 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

- All have the same potential difference
- Capacitances add
- (conceptually add A’s)

- All have the same charge separation
- Reciprocals are additive
- (conceptually add d’s)

- e0 = 8.8510–13

C2

N m2

- 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

Shell Area = 4pr2

FE = q/e0 = EA

+q

E =

=

s

1

sA

FE =

, so E =

e0

2

e0

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

Individually

Together

- Field E =

=

s

Q

e0

Ae0

Qd

- Potential DV = Ed =

Ae0

Q Ae0

Ae0

- Capacitance Q/DV =

=

Qd

d

- Plate area A, plate separation d