Capacitance and Dielectrics Chapter 241 Any two conductors separated by an insulator forms a Capacitor. Definition: 1F =1 farad = 1 C/V = 1 coulomb /volt.

Capacitance and Dielectrics

Chapter 24 1

Any two conductors separated by an insulator forms a Capacitor.Definition:

1F =1 farad = 1 C/V = 1 coulomb /volt

ab

QC

V

Chapter 24 2

Capacitors and Capacitance (Chapter 24, Sec 1)

Figure 24-2

A

QE

00

A

Q

QA

dd

A

QEdVab

00

abab CVVd

AQ 0

Coul/m2

Farads

1 F = 1 x 10-6 Farads

1 pF = 1 x 10-12 Farads

1 nF = 1 x 10-9 Farads

Chapter 24 3

12 2 2

2

120

0

1 1 .

1 /

1 /

1 V = 1J/C

/ .

1 F 1 C/V

1 F 1 C /J

8.85 10 /

8.85 10

J N m

E N C

E V m

C N m

x F m

x

Useful Definitions and Relationships

Chapter 24 4

Practical Capacitors

Practical Values100µF1µF0.01µF100pF1pF

Some examples of flat, cylindrical, and spherical capacitors

– See just how large a 1 F capacitor would be. Refer to Example 24.1.

– Refer to Example 24.2 to calculate properties of a parallel-plate capacitor.

– Follow Example 24.3 and Figure 24.5 to consider a spherical capacitor.

– Follow Example 24.3 and Figure 24.5 to consider a cylindrical capacitor.

Chapter 24 6

Capacitors in Series

11 C

QV

22 C

QV

212121

11

CCQ

C

Q

C

QVVV

21

11

CCQ

V

V

QCeq

Q

V

Ceq

1

21

111

CCCeq

All capacitors in series have the same charge Q

Chapter 24 7

Capacitors in ParallelAll Capacitors in Parallel have the same voltage V

Figure 24-7

VCQ 11 VCQ 22

VCCVCVCQQQ 212121

21 CCV

Q

21 CCV

QCeq

Chapter 24 8

Capacitors in Series and Parallel - Example 24.6

Chapter 24 9

Energy Storage in Capacitors

Let q equal the changing charge increasing from 0 to Q as the changing voltage v is increasingfrom 0 to Vab. We will determine the energy stored in the capacitor when the charge reaches Qand the voltage reaches Vab. (q and v are the intermediate charge and charging voltage

q

wv vqw v

qC

C

qv vdqdw

C

Qq

Cqdq

CdqC

qvdqW

QQQQ

22

11 2

0

2

000

joules

Chapter 24 10

Example 24-7, Page 827 Text Transferring charge and energy between capacitors

Calculate the initial chargeCalculate the initial stored energyConnect the capacitorsCalculate the resulting voltageCalculate the charge distributionCalculate the energy change

Chapter 24 11

Capacitor Dielectrics Solve Three Problems

1. Provides mechanical spacing between two large plates2. Increases the maximum possible potential between

plates.3. For a given plate area the dielectric increases the

capacitance.

Dielectrics change the potential difference

• The potential between to parallel plates of a capacitor changes when the material between the plates changes. It does not matter if the plates are rolled into a tube as they are in Figure 24.13 or if they are flat as shown in Figure 24.14.

Chapter 24 13

What Happens with a Dielectric

Figure 24-12

V V0 (Q unchanged)

AA

C0

C

00 V

QC

V

QC

Therefore: C C0

0C

CK (Definition of Dielectric Constant) (24-12)

V

V

C

CK 0

0

K

VV 0 (24-13)

Dielectric Constants

Field lines as dielectrics change• Moving from part (a) to

part (b) of Figure 24.15 shows the change induced by the dielectric.

Chapter 24 16

Induced Charge and Polarization

Inserting the dielectric increases permittivity by K, decreases E by 1/K and decreases energy density by 1/KThe E field does work on the dielectric as it is inserted. Removing the dielectric the energy is returned to the field.

Chapter 24 17

Dielectrics (Chapter 24, Sec 4)Induced Charge and Polarization

E

E

Ed

dE

V

V

C

CK 000

0

Therefore: E E0

0

0

KK

EEKEE 0

0 iE

00

E (24-15)

(24-18)

0

Chapter 24 18

Dielectric Breakdown

d

V = Ed

Vmax = Emax d

For dry air: Emax = 3 x 106 V/m

For Mylar, K=3.1, Emax = 9.3 x 106 V/m

where Emax is the dielectric strength of the dielectricin volts/meter.

Dielectric breakdown• A very strong electrical field can exceed the strength of the

dielectric to contain it. Table 24.2 at the bottom of the page lists some limits.

Electric Field Effect on Molecules

Polarization and electric field lines

Chapter 24 22

Chapter 24 23

Chapter 24 24