Capacitors

1. Capacitors

2. Capacitors
•A capacitor is a device that stores electric
charge.
•A capacitor consists of two conductors
separated by an insulator.
•Capacitors have many applications:
–Computer RAM memory and keyboards.
–Electronic flashes for cameras.
–Electric power surge protectors.
–Radios and electronic circuits.

3. Types of Capacitors
Parallel-Plate Capacitor Cylindrical Capacitor
A cylindrical capacitor is a parallel-plate capacitor that has
been rolled up with an insulating layer between the plates.

4. Capacitors and Capacitance
Charge Q stored:
CVQ=
The stored charge Q is proportional to the potential
difference V between the plates. The capacitance C is
the constant of proportionality, measured in Farads.
Farad = Coulomb / Volt
A capacitor in a simple
electric circuit.

5. Parallel-Plate Capacitor
•A simple parallel-plate
capacitor consists of
two conducting plates
of area A separated by
a distance d.
•Charge +Q is placed
on one plate and –Q on
the other plate.
•An electric field E is
created between the
plates.
+Q -Q
+Q -Q

6. What is a capacitor?
•Electronic component
•Two conducting surfaces separated by an insulating
material
•Stores charge
•Uses
–Time delays
–Filters
–Tuned circuits

7. Capacitor construction
•Two metal plates
•Separated by insulating
material
•‘Sandwich’ construction
•‘Swiss roll’ structure
•Capacitance set by...
d
A
Ce=

8. Defining capacitance
•‘Good’ capacitors store a lot of charge…
•…when only a small voltage is applied
•Capacitance is charge stored per volt
•Capacitance is measured in farads F
–Big unit so nF, mF and mF are used
V
Q
C=

9. Graphical representation
Equating to the equation of a straight line
mxy
CVQ
V
Q
C
=
=
=
Q
V
Gradient term is
the capacitance
of the capacitor
Charge stored is
directly
proportional to
the applied
voltage

10. Energy stored by a capacitor
•By general definition E=QV
–product of charge and voltage
•By graphical consideration...
QVE
2
1
=
Area term is
the energy
stored in the
capacitor
Q
V

11. Other expressions for energy
•By substitution of Q=CV
C
Q
E
CVE
QVE
2
2
2
1
2
1
2
1
=
=
=

12. Charging a capacitor
•Current flow
•Initially
–High
•Finally
–Zero
•Exponential model
•Charging factors
–Capacitance
–Resistance
I
t

13. Discharging a capacitor
•Current flow
•Initially
–High
–Opposite to
charging
•Finally
–Zero
•Exponential model
•Discharging factors
–Capacitance
–Resistance
I
t

14. Discharging a Capacitor
•Initially, the rate of discharge is high because the
potential difference across the plates is large.
•As the potential difference falls, so too does the
current flowing
•Think pressure
As water level
falls, rate of
flow decreases

15. •At some time t, with charge Q on the
capacitor, the current that flows in an
interval Dt is:
I = DQ/Dt
•And I = V/R
•But since V=Q/C, we can say that
I = Q/RC
•So the discharge current is proportional to
the charge still on the plates.

16. •For a changing current, the drop in
charge, DQ is given by:
DQ = -IDt (minus because charge Iarge
at t = 0 and falls as t increases)
•So DQ = -QDt/RC (because I = Q/RC)
•Or -DQ/Q = Dt/RC

17. V
or
Q
t
V
or
Q
t
Voltage and charge characteristics
•Charging Discharging
RC
t
eQQ
-
=
0)1(
0
RC
t
eVV
-
-=

18. Dielectrics
•A dielectric is an insulating material (e.g.
paper, plastic, glass).
•A dielectric placed between the conductors of
a capacitor increases its capacitance by a
factor κ, called the dielectric constant.
C= κC
o
(C
o
=capacitance without
dielectric)
•For a parallel-plate capacitor:
d
A
d
A
C e
e
k ==
0
ε = κε
o
= permittivity of the material.

19. Properties of Dielectric Materials
•Dielectric strength is the maximum electric field that a
dielectric can withstand without becoming a conductor.
•Dielectric materials
–increase capacitance.
–increase electric breakdown potential of capacitors.
–provide mechanical support.
Dielectric
Strength (V/m)
Dielectric
Constant κ
Material
3 x 10
6
1.0006 air
8 x 10
6
300 strontium titanate
150 x 10
6
7 mica
15 x 10
6
3.7 paper

20. Practice Quiz
•A charge Q is initially placed on a parallel-plate
capacitor with an air gap between the electrodes,
then the capacitor is electrically isolated.
•A sheet of paper is then inserted between the
capacitor plates.
•What happens to:
a)the capacitance?
b)the charge on the capacitor?
c)the potential difference between the plates?
d)the energy stored in the capacitor?

21. Capacitors in Parallel
VC
VCCC
VCVCVC
QQQQ
eq
=
++=
++=
++=
)(
321
321
321
...
321 +++= CCCC
eq
Capacitors in Parallel:

22. Capacitors in Series
eqC
Q
CCC
Q
C
Q
C
Q
C
Q
VVVV
=
÷
÷
ø
ö
ç
ç
è
æ
++=
++=
++=
321
321
321
111
...
1111
321
+++=
CCCC
eq
For n capacitors
in series:

23. Circuit with Capacitors in Series and
Parallel
a b
15 μF3 μF
6 μF
What is the effective capacitance C
ab
between points a and b?
20 μF
C
1
C
2
C
3
C
4
C
ab
?

24. •Product of
–Capacitance of the capacitor being charged
–Resistance of the charging circuit
–CR
•Symbol t ‘Tau’
•Unit seconds
Time constant
tCR
tQ
V
V
Q
CR
=
¸
´=

25. When t equals tau during discharge
•At t = tau the capacitor
has fallen to 37% of its
original value.
•By a similar analysis tau
can be considered to be
the time taken for the
capacitor to reach 63% of
full charge.
37.0
0
1
0
0
0
´=
=
=
=
-
-
-
QQ
eQQ
eQQ
eQQ
RC
RC
RC
t

26. Graphical determination of tau
•V at 37%
•Q at 37%
•Compared to initial
maximum discharge
V
or
Q
t
R
t
C
RCt
t
=
=
=t

27. Logarithmic discharge analysis
•Mathematical
consideration of discharge
•Exponential relationship
•Taking natural logs
equates expression to
‘y=mx+c’
•Gradient is -1/Tau
0
0
0
0
ln
1
ln
lnln
Vt
RC
V
RC
t
VV
e
V
V
eVV
RC
t
RC
t
+
-
=
-
=-
=
=
-
-

28. Logarithmic discharge graph
lnV
t
Gradient term
is the -1/Tau

29. www.search for...
•Capacitors