Capacitor

Function?

- To store electric

charge

symbol?

Capacitance

A measure of how

much a capacitor can

store charge V

QC =

Capacitance, Farad (F)

Magnitude of

charge in either

plate

Coulomb (C)

Potential

different

between plate,

Volt (V)

Basic Structure

A Pair of conducting

plates separated by an

insulator (dielectric)

Parallel plate Capacitor

Air, vacuum

A = area of plate surface

d = Distance between plates

Quantity Unit Equations

Electric Field, E (V/m)

(Volt/meter)

Capacitance, C (F) Farad

Surface Charge

Density, σ(C/m2 )

(Coulomb/meter2)

===A

QE

00 εε

σ

d

V

V

EA

V

QC 0ε

==

d

A0ε=

A

Q=σ

12

o(8.85 10 F /m)−

ε = ×

Example 1

• a) if the charge on a capacitor is 75µC when

the voltage across it is 50V, what is the

capacitor’s capacitance?

• b) if the voltage across this capacitor is

increased to 125V, what is the charge on the

capacitor?

Example 2

• a) what is the capacitance of a parallel plate

capacitor that has square plates with lateral

dimensions of 129 mm on one side, a plate

separation of 0.39 mm and vacuum between

the plates?

• b) what is the charge on the capacitor if the

potential difference across it is 45V?

Example 3

• The plates of parallel plate capacitor are in

vacuum, 7mm apart and 2.0m2 in area. A

potential difference of 10kV is applied across

the capacitor. Compute

a) The capacitance of the capacitor

b) The charge on each plate

c) The magnitude of the electric field in the

space between the plates.

Effect of a Dielectric MaterialWhy dielectric material?

To increase

capacitance

of capacitorAllow capacitor

to be built in

practical shapes

and sizes

To limit the

potential

difference that can

be applied

between plates,

Vmax (Breakdown

potential)

Dielectric Constant, K- The properties of dielectric material

Material Dielectric constant, K Dielectric

strength(kV/mm)

Vacuum 1

Air (STP) 1.000576 3

Polystyrene 2.6 24

Ebonite 3

Paper 3.5 16

Pyrex 4.7 14

Mica 7

Water 80

Quantity unit Equations

Dielectric

Constant,

K

-

0ε

ε=

0C

CK =

V

V0=

E

E0=

C = The capacitance when the dielectric material is between the plates

Co = The capacitance when there is air or vacuum between the plates.

V = The potential difference between the plates with the dielectric

Vo = The potential difference between the plates without the dielectric

Quantity Equation For Capacitor

without dielectric material

(vacuum/air)

Equations for Capacitor with

dielectric Material

Electric Field, E

Capacitance, C

Surface Charge

Density, σ

0 00

0 0

QE

A

σ= = =ε ε

0V

d

QE

A

σ= = =ε ε

V

d

0 0 00

0 0

Q E AC

V V

ε= =

d

A0ε=

Q EAC

V V

ε= =

A

d

ε=

00

Q

Aσ =

Q

Aσ =

Example 4

A parallel plate capacitor having area 40 cm2 and

spacing of 1 mm is charged to a potential difference of

600V. Find

a) the capacitance of the capacitor

b) the magnitude of charge on each plate

d) the electric field between the plate

e) the capacitance of the capacitor if the dielectric

between the capacitor is 1.4

Example 5

The electric field between the plates of a paper

separated (K=3.75) parallel plate capacitor is 10.17 x

104 V/m. The plates are 2.01 mm apart and the

charge on each plate is 0.829 µC. Determine;

a) the capacitance of the capacitor

b) The area of each plate

Example 6

A 7µF capacitor with air between the metal plates is

connected to a 45V battery. The battery is then

removed, leaving the capacitor charged.

a) Calculate the charge on the capacitor

b) The air between the plates is replaced by oil with

K=2.1. Find the new value of the capacitance, the

new potential difference in the capacitor.

Series Parallel

VS = V1 + V2 + V3 V1 = V2 = V3 = V

1/Ceq = 1/C1 + 1/C2 + 1/C3 Ceq = C1 + C2 + C3

Qeq = Q1 + Q2 + Q3Q1 = Q2 = Q3 = Q

Capacitor in Series and ParallelQ1 Q2 Q3

the charges are the same on all plates

⇒ Q1 = Q2 = Q3 = Q

The sum of voltage drop across all capacitors

equals the voltage of the source =>

VS = V1 + V2 + V3

Total Capacitance for Series Circuit =>

= + +

e q 1 2 3

1 1 1 1

C C C C

Q1

Q2

Q3

The total charges is the sum of the

charges of individual capacitors

⇒ Q1 = Q1 +Q2 + Q3

the voltage across the capacitors is the same.

V1 = V2 = V3 = V

Total Capacitance for Parallel Circuits

Ceq = C1 + C2 + C3

Energy Stored in a Charged

Capacitor

C2

QU

2

= QV2

1CV

2

1U 2

==

The work that is done in charging the

capacitor is stored in the form of electrical

potential energy.

The electrical potential energy stored in

a charged capacitor is :-

Example

Answers: i)C234=8µF, Ctotal= 2.22 x 10-6F , ii) V234=V2= 3.3375V, iii) Q1=Q5=2.67 x 10

-5C,

Q2 = 1.00x10-5 C, Q3= 3.3375x10

-6C, Q4= 1.335x10-5 C.

Answers: i) CT= 6µF, ii) QT=1.2x10-11C, Q3=Q6=2.4 x 10

-5C, Q4= 4.8x10-5 C, iii)

V4=12V, V3=8V, V6=4V

Different types of capacitors: From left:

multilayer ceramic, ceramic disc, multilayer

polyester film, tubular ceramic, polystyrene,

metalized polyester film, aluminum

electrolytic. Major scale divisions are in

centimetres.