L

A

AQLQ

V

QC 0

0

Capacitors in series: ...1111

321

CCCCtot

Capacitors in parallel: ...321 CCCCtot

22

2

1

2

1Q

CCVW

faradC ][

CapacitorsConsider two large metal plates which are parallel to each other and separated by a distance small compared with their width.

Area A

The field between plates is 0

E

VL

y

LdydyEbottomVtopVLL

y00 00

)]()([

A

QLL

A

ALbottomVtopV

000

)]()([

0AQL

V

The capacitance is:

L

A

AQLQ

V

QC 0

0

a

b

C1C3

C5C4

C2

C1=C5=8.4 F and C2=C3=C4=4.2 F The applied potential is Vab=220 V. a)What is the equivalent capacitance of the network

between points a and b? b) Calculate the charge on each capacitor and the

potential difference across each capacitor.

ticselectrostainrdE 0

E

0 rdE

0 rdE

1E

2E

0)()( 2121 CDEABErdErdED

C

B

A

A

B C

D

!21 impossibleEE

Electric field near the surface of a conductor

0

E

L

A

AQLQ

V

QC 0

0

Capacitors in series: ...1111

321

CCCCtot

Capacitors in parallel: ...321 CCCCtot

22

2

1

2

1Q

CCVW

faradC ][

Most capacitors have a non-conducting material, or dielectric, between their conducting plates. When we insert an uncharged sheet of dielectric between the plates, experiments show that the potential difference decreases to a smaller value V (we did this experiment last class !).

dielectricwithoutV

QC

00

dielectricwithV

QC

0CC

When the space between plates is completely filled by the dielectric, the ratio

0C

CK is called dielectric constant.

Moore’s Law (1965): every 2 years the number of transistors on a chip is doubled

Smaller, Denser, Cheaper