Capacitor by Anurag

8/6/2019 Capacitor by Anurag

1/19

CAPACITORS


2/19

ELECTRIC FIELD STRENGTH

What is it? ANS:Is the force that an electric charge

experiences within a specific space(field).

E = F/q

Symbol: E Units:Newtons perCoulomb (NC-1)

Remember that electric fields act either inwardoroutwards

dependent on thecharge:

+ -

Field lines represented

with an arrow henceare vectors.

Field lines are stronger

when closer together.


3/19

FIELD LINES BETWEEN PLATES

If parallel plates are charged then a uniform electric field is then

established:

- - - - - - - - - - - - - - - - - - - -

+ + + + + + + + + + + + + + + + + +

Note:

The field strength is the same wherever the charge happens to be

e.g. A; B or C.

BA

C

At the edges D the field strength is weakeras the field lines are

longer, the plates being further apart.

D

If a charge is moved from the negative plate

to the positive then potential energy (EP) is

produced or a potential difference set up V.

This is also dependent on the distance d

between the plates thus two equations can

be produced:

EP = qV

E = V/d


4/19

CAPACITORS

What is it? ANS:It is an electrical component that can

store electrical charge and release itsome time later.

Symbol:C Units: Farad (F)

USES

1. Storing energy as in flashphotography

2. Time delays in electroniccircuits

3. As filters in electronic circuits

4. In tuning circuits

Often made like a swiss

roll by rolling metal plates

with a insulator (dielectric)

in between and wires

attached to each plate.

CEveryday capacitors are measured in either

QF (10-6); nF (10-9); pF (10-12).


5/19

BASIC CONSTRUCTION

INSULATOR

(DIELECTRIC)

CONDUCTOR CONDUCTOR

+-

TWO

OPPOSITELY

CHARGED

CONDUCTORSSEPARATED

BY AN

INSULATOR -

WHICH MAYBE AIR

The Parallel Plate Capacitor


6/19

WHAT DOES A CAPCITOR DO?

+

+

+

+

+

+

+

+

-

-

-

-

-

-

-

-

+-

The battery causes the

flow of electrons to

accumulate on one plateand attracts an equal

number of electrons fro

the other plate, leaving the

plates oppositely charged.

When fully charged:

Flow of e- stops.

Both plates equal &

oppositely charged.

Pd across plates, V =

Vsupply.

Electric field, E exists

between plates E = V/d.

dE = electric field strength


7/19

CAPACITANCE

This is the amount of charge a capacitor can store when connected

across a potential difference of 1 volt. Obviously the larger the

capacitor the more charge it can contain.

The capacitance (C) of a capacitor which stores a charge, Q

coulombs on each plate when connected across a supply of volts, V,

is given by:

C = Q/V

Capacitors have a finite voltage at which they work at. If the voltage is

exceeded then the dielectric will melt and the plates suddenly come

into contact. Short circuit, capacitor explodes!!

BOOM


8/19

Charge stored [Q] depends on p.d. [Volts] applied [V]

Q

V

Gradient = C

Remember that the capacitance, C, is defined as

the charge required to raise the potential by one voltthe charge required to raise the potential by one volt

Hence C = Q/V


9/19

WHAT FACTORS DETERMINE CAPACITANCE?

Depend upon three factors:

1. The area, A, of the parallel plates.

2. The distance, d, separating the plates.

3. The properties of the dielectric material

between the plates.

1. Plates that

have a greater

area can store

more charge,

thus:

2. Plates that are

closer

together can

store more

charge, thus:

C w A C w 1/d

C = constant x A/d

Constant = absolute

permittivity of free

space (Io)

I0 = 8.84x10-12 Fm-1

C = (IoA)

d


10/19

Area ofPlate overlap

= A

dd = plate separation

Medium relativepermittivity = Ir

d

AC

rII0

!

I0 = the permittivity of freespace = 8.86. X 10-12 F m-1

For air or a vacuum, Ir = 1

THE DIELECTRIC CONSTANT:

Different materials insulate at

differing amounts thus changing

the capacitance, called dielectric

effect. The dielectric constant (Ir)gives the proportion by which C

increases when dielectric placed

between the plates.


11/19

The dielectric constant does not a have a unit as it is the ratio

between two capacitance values:

Ir= Cdielectric

Cair

Examples of dielectric

constants include:

Dielectric material IrAir 1.0

Oiled paper 2.0

Polystyrene 2.5

Glass 6.0

Water 80


12/19

THE ENERGY STORED IN CAPACITOR:

As charge, Q, is packed onto the plates work needs to be done.

Repulsive forces want to push the electrons away from the negativeplate towards the positive. The battery supplies the push, energy, to

pack these electrons. The push, pd, the battery has the greater the

capacitance, C. Thus energy provided by the cell must equal:

E = Q x V

Area undergraph= energychange

= Q x V

Q

V

For a

capacitor

V vs Q isa straight

line

graph

V

Q

Area

under

graph =

x Q x V

Energy provided by cell Energy stored in capacitor


13/19

As capacitance is the amount of

stored charged then the energy

inside a capacitor then two

formulae can be produced.

EP = CV2 [Substituting Q = CV into EP = QV]

EP = Q2/C [Substituting V = Q/C into EP = QV]


14/19

CAPACITORS IN SERIES & PARALLEL:

+-

Q- Q-Q+ Q+

C1 C2

V2V1

V

Charge on each capacitor is

the same.

V = V1 + V2

For two or more capacitors:

1 = 1 + 1 .

Cs C1 C2

SERIES PARALLEL

+-

V

C1

C2

Q1

Q2

Voltage across each capacitor

same as, V, of cell.

Q = Q1 + Q2

For two or more capacitors:

Cp = C1 + C2 .


15/19

RC CIRCUITS

CHARGING A CAPACITOR:

An RC circuit is one that contains a resistor, R and a capacitor, C.

R

CV

CURRENT:

When a capacitor begins to charge there is a massive flow of charge

to the negative plate. This then decreases with time as repulsion

from that plate pushes electron away.

VOLTAGE:When the capacitor is empty there is zero charge stored. As

electrons rush in there is a huge build up of energy. This begins to

level out as repulsion denies entry of any further charge.


16/19

Imax

time0

From this two graphs can be drawn for the charging of a capacitor

with relation to what happens to current I and voltage V.

Volts

VC

Amps

Current starts at maximum Imax

and then decreases to zero asthe negative plate fills up with

negative charge. Repulsion

pushes against the force of

the battery

Voltage starts at zero and

rapidly increases until itbegins to reach maximum.

Now repulsion prevents any

further charge entering so the

energy remains constant.

CURRENT GRAPH VOLTAGE GRAPH


17/19

DISCHARGING A CAPACITOR:

When a capacitor discharges the voltage and current graphs are the

same. They start at a maximum and follow the inverse curves downtowards zero, although it is worth noting that they dont reach zero.

Volts, V

Time, t0

V0

Current I

Time, t

I0

Explain what is happening in each of thesegraphs andwhy

they are the same.


18/19

TIME CONSTANT:

Time constant is the measure of time it takes for a capacitor to reach

63% of the total amount of voltage or current that it can store/releasedepending on whether it is charging/discharging. The largerX, the

slower the process.

It is given the term tau, X and is measured in seconds, s. The

formula for time constant is:

X = RC

Where:

X = time constant (s)

R = resistance ()

C = capacitance (F)As the voltage never reaches max orAs the voltage never reaches max or

zero, then the total time taken cant bezero, then the total time taken cant be

measured hence that is why 63% of themeasured hence that is why 63% of thetime is used. (time is used. (Same for currentSame for current))


19/19

Volts

63%

VOLTAGE GRAPH

Time, t

Vmax

X

100%

86%

2X

This works exactly thesame for discharging and

for current they are just

reversed.

The second time constant

is 63% of what is left.

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Capacitor by Anurag