CAPACITORS

1
CAPACITORS
C A P A C I T O R S
Prepared By Mr Tan Kia Yen
2
Assessment Objectives
C A P A C I T O R S
(a) understand the function of capacitors in
simple circuits. (b) define capacitance and the
farad. (c) recall and use C Q/V. (d) derive,
using the formula C Q/V, conservation of charge
and the addition of potential differences
formulae for capacitors in series and parallel.
3
C A P A C I T O R S
Assessment Objectives
(e) use formulae for capacitors in series and
parallel. (f) use the area under a
potential-charge graph to derive the equation W
½QV and hence W ½CV2.
4
C A P A C I T O R S
Assessment Objectives
QCV
COQ
5
C A P A C I T O R S
Introduction
A capacitor is any device that consists of two
conductors isolated from each other so that they
can hold equal but opposite charges. The circuit
symbol for a capacitor is
A capacitor can be used to store electrical
charges and hence, electrical energy.
6
C A P A C I T O R S
Introduction
Ceramic Capacitors
7
C A P A C I T O R S
Introduction
Electrolytic Capacitors
Polarity must be observed.
8
C A P A C I T O R S
Introduction
Chip Capacitors
9
Common applications
C A P A C I T O R S

• Tuning circuits
• A. C. rectification
• Ignition system
• Energy storing device

10
C A P A C I T O R S
Capacitance
Although any conductor can be a capacitor,
practical capacitors are made up of two parallel
conducting plates separated by an insulator or
dielectric (e.g mica, paper, oil or air).
11
C A P A C I T O R S
Capacitance
A capacitor is device for storing electric
charges.
Air, paper, mica, ceramic
12
C A P A C I T O R S
Safe Voltage
If the potential difference across the two plates
is too high, the dielectric will breakdown and
allow a current to pass through it.
V
Hence, capacitors are marked with the highest
safe voltage which can be used across them.
13
C A P A C I T O R S
Capacitance
A capacitor can be charged by simply connecting
its plates to a battery as shown in the diagram
below.
As V increases, I decreases. When V Vo , I 0
More (charging)
14
C A P A C I T O R S
Capacitance
The magnitude of the charge on each conductor is
proportional to the potential difference. Q? V
Q CV
where C is the constant of proportionality
which depends on the shape and size of the
conductor and is called its capacitance.
15
C A P A C I T O R S
Capacitance
The capacitance of a parallel plate capacitor is
defined as the ratio of the charge stored on
either plate to the potential difference across
the plates.
Mathematically, it is defined as C Q/V
The larger the capacitance, the larger the charge
the capacitor can store for a given potential.
16
C A P A C I T O R S
Capacitance
Unit of capacitance farad (F)
A parallel plate capacitor has a capacitance of
one farad if the charge on either of the plate is
one coulomb when the potential difference across
the plates is one volt. A farad is a very large
unit.
Mircro farad 1 ?F 10-6 F Pico farad
1 pF 10-12 F
17
C A P A C I T O R S
Capacitors in parallel
C1
Q
- Q
C2
C
C3
18
C A P A C I T O R S
Capacitors in parallel
The p.d. across each capacitor is the same. Q1
C1V Q2 C2V Q3 C3V
C1
C2
C3
19
C A P A C I T O R S
Capacitors in parallel
Total charge Q Q1 Q2 Q3 C1V
C2V C3V If C total capacitance then
Q CV So CV C1V C2V C3V
C1
C2
C3
C C1 C2 C3
Q Q1 Q2 Q3
20
C A P A C I T O R S
Capacitors in series
Q
-Q
Q
Q
V
C
-Q
-Q
Q
-Q
21
C A P A C I T O R S
Capacitors in series
The charge on each capacitor is the same. V V1
V2 V3
Q Q1 Q2 Q3
22
C A P A C I T O R S
Examples
Four identical capacitors are connected as shown.
Which of the following lists the arrangements in
order of decreasing capacitance ?
C/4
4C
Ans B PSRQ
2C/5
3C/4
23
C A P A C I T O R S
Examples
Find the equivalent capacitance between points A
and B for the following network.
Solution
C1 2.0 ?F

C2C3
C


3
5.0 V
5.0 5.0 10.0 µF
C2 5.0 ?F
C3 5.0 ?F
1
1
1


C1
C
Ceq
C1
1
1
5.0 V


.
0
2
10.0
C
µF
Ceq
1.67
24
C A P A C I T O R S
Examples
Find the equivalent capacitance between points A
and B for the following network. If the p.d.
across AB is 12.0 V, what is the charge on C2?
Solution
Let C be the equivalent capacitance of C1, C2
and C3.
25
C A P A C I T O R S
Examples
C C1 C2 C3
Q Q1 Q2 Q3
Q
Q
Q


3
2
1
V
C
V
C
V
C


3
3
2
2
1
1
V
)
C
C
(


2
3
2
V
)
.
.
(
V
.
0
1

0
2

0
6
2
1
)
.......(
V
.
V
1
50
0

2
1
)
......(
.
V
V
2
0
12


2
1
)
(

)
(
solving
2
1
V
.
V
0
8

2
V
C
Q

2
2
2
6
-
)
.
)(
.
(
0
8
10

0
2

m
F
16

26
C A P A C I T O R S
Energy storage in capacitor
When charging a capacitor, work has to be done
against

• attractive forces when removing electrons from
  the positive plate.
• repulsive forces when adding electrons to the
  negative plate.

The work is stored as potential energy in the
electric field between the plates
27
C A P A C I T O R S
Energy storage in capacitor
To add charge ? q to the capacitor when the p.d.
is v, work done v ? q When full charge Q is
added, total work done area under the graph
28
C A P A C I T O R S
Energy storage in capacitor
29
C A P A C I T O R S
Energy storage in capacitor
Work done by battery QV Energy stored in
capacitor ½ QV Loss of energy ½ QV The
energy is lost within the resistance of the
circuit as heat.
30
C A P A C I T O R S
Examples
A capacitor of capacitance 160 ?F is charged to a
p.d. of 200 V and then connected across a
discharge tube, which conducts until the p.d.
across the capacitor has fallen to 100 V.
Calculate the energy dissipated in the tube.
Solution
Energy dissipated ½ CVi 2 - ½ CVf 2 ½ C (Vi
2 - Vf 2 ) ½ ? 160 ? 10-6 (2002 - 1002) 2.4
J
31
C A P A C I T O R S
Connecting a Charged Capacitor to an Uncharged
Capacitor
10 C
6 C
4 C

• Final P.d. across both capacitors is the same.
• Total charge before and after connection is
  conserved. (Q1 Q2 Qo)
• Total energy stored in capacitors is not
  conserved.

32
C A P A C I T O R S
Examples
A capacitor of capacitance C is charged to a p.d.
of Vo. The charging battery is now removed. A
second uncharged capacitor of capacitance 2C is
now joined to C. What is
(a) the final p.d. across the combination?
Solution

• By conservation of charge,

33
C A P A C I T O R S
Examples
(b) the initial total energy of the capacitors?
Solution
(b)
34
C A P A C I T O R S
Examples
(b) the final total energy of the capacitors?
Solution
35
C A P A C I T O R S
Examples
In the circuit shown, a 3.0 ?F capacitor is
charged from a 6.0 V battery. The switch is then
reconnected to charge the 1.0 ?F capacitor from
the 3.0 ?F capacitor. Calculate
(ai) the charge and energy initially stored in
the 3.0 ?F capacitor.
Solution
36
C A P A C I T O R S
Examples
(aii) the final charge and energy stored in each
capacitor.
Solution
37
C A P A C I T O R S
Examples
Solution (contd)
Total energy stored in the capacitors
38
C A P A C I T O R S
Examples
(b) Account for the difference in the total
energy stored in the capacitors in (i) and (ii).
Solution
(b) The difference in energy represents the
energy lost as heat due to the resistance in the
circuit.
39
C A P A C I T O R S
Two Charged Capacitors are connected together

• When plates of the same sign are connected
  together, the total charge stored in the two
  capacitors before and after connection is
  conserved.
• Q1 Q2 Q1 Q2
• When plates of the opposite signs are connected
  together, the total charge after connection is
  equal to the difference of the charges stored in
  each capacitor before connection.
• Q1 - Q2 Q1 Q2

40
C A P A C I T O R S
Examples
A 2.40 ?F capacitor is charged to 200 V and a
1.10 ?F capacitor is charged to 60.0 V. The two
capacitors are connected together such that their
positive plates are joined together and the same
applies for their negative plates. What is the
p.d. and the charge across each capacitor?
41
C A P A C I T O R S
Examples
Solution
C1
Q1
-Q1
V1
V2
Q2
-Q2
C2
42
C A P A C I T O R S
Examples
C1
Q1
-Q1
Solution
V1
Both capacitors have the same final p.d. V
V2
By conservation of charge,
Q2
-Q2
C2
43
C A P A C I T O R S
Examples
C1
Solution
Q1
-Q1
V1
V2
Q2
-Q2
C2
44
C A P A C I T O R S
Examples
If the capacitors in the previous example are
connected such that oppositely charged plates are
now joined together, what is the p.d. and the
charge across each capacitor?
C1
Q1
-Q1
Solution
V1
V2
-Q2
Q2
C2
45
C A P A C I T O R S
Examples
Solution
C1
Q1
-Q1
By conservation of charge,
V1
V2
-Q2
Q2
C2
46
C A P A C I T O R S
Charging and Discharging a Capacitor
VC VR Vo At t 0, C is uncharged. Q 0 VC
0, VR Vo I VR /R Vo /R
As capacitor charges up, VC?, VR ? and I ?
More ( V graph)
More ( V graph, charging discharging)
More ( V graph)
47
C A P A C I T O R S
Charging and Discharging a Capacitor
As t ? ?, C becomes fully charged. VC Vo , VR
0 and I 0
where
I Io e-t/RC , VC Vo(1 - e-t/RC) , Q
Qo(1 - e-t/RC)
Io Vo /R Qo CVo
48
C A P A C I T O R S
Charging and Discharging a Capacitor
During discharging, VC VR At t 0, C is fully
charged. VC Vo and so VR Vo I VR /R Vo
/R
C
R
VR
As capacitor discharges, VC ?, VR ? and I ? As t
? ?, C becomes completely uncharged. VC 0 , VR
0 and I 0
49
C A P A C I T O R S
Charging and Discharging a Capacitor
C
R
VR
where
I Io e-t/RC , VC Voe-t/RC , Q
Qoe-t/RC
Io Vo /R Qo CVo
More ( circuit)
50
C A P A C I T O R S
The End