Capacitors and dielectris
Chapter
3 1
Chapter
capacitors
A capacitor consists of two conductors (with area A)
that are close together, but not touching
(at distance d).
A capacitor has the ability to store electric charge.
(a)
(b)
When a capacitor is connected to a battery,
the charge on its plates is proportional to the
voltage:
q = CV
The quantity C is called the
capacitance.
Figure (a) shows a parallel plate capacitor
connected to a battery,
and (b) is the corresponding circuit diagram.
The unit of capacitance
is the farad (F): 1 F = 1 C/V
capacitance of a parallel plate capacitor
For a parallel plate capacitor as shown,
the field between the plates is:
E
q
0 A
The potential difference between the plates is:

Vba 
qd
0 A
The capacitance of a parallel plate capacitor is therefore:

C

q
A
 0
V
d
capacitance of a spherical capacitor
The potential of a spherical conductor is given by:
V
1 q
4 0 r
And the capacity of a spherical conductor is therefore:

C
q
 4 0 r
V
The amount of charge stored on a spherical conductor is directly proportional

to the radius.
What is the capacitance of the Earth?
Assuming the Earth to be a sphere with a radius of 6,400 km, its capacitance
in vacuum is:


CE  4 0  6.4 106 m  7.1104F
A 1 F capacitor has a much larger capacitance than the Earth!

capacitors in series and in parallel
Capacitors in parallel have the same voltage
across each individual capacitor.
The equivalent capacitor is one that stores
the same charge when connected
to the same battery:
Ceq  C1 C2 C3

Capacitors in series have the same charge.
In this case, the equivalent capacitor has the
same charge for the same voltage difference.
The inverse of the equivalent capacitance
is therefore given by the sum of the inverses
of the individual capacitances:
1
1 1
1
 

Ceq C1 C2 C3
capacitors in our life
Flash lamps
require a very
high current over
a very short time
period to operate,
photoflash
capacitors are
designed for this
purpose.
Heart
defibrillators
use an
electrical
discharge to
“jump-start”
the heart, and
therefore to save
lives.
Touch screen panels makes use of capacitors. They consists
of an insulator, glass for example, coated with a transparent
conductor. The human body is a good electrical conductor and
when the surface of the screen is touched by the fingers
there is a variation in the screen’s capacitance,
which is detected.
dielectric
A dielectric is an insulator, and is characterised by a dielectric constant κ.
The capacitance of a parallel plate capacitor filled with a dielectric is:
C  0
A
d
where κ is the dielectric constant of the medium relative to the vacuum.
Using the dielectric constant, the absolute permittivity of the dielectric is defined as:

  0

If a material contains
polar molecules, they
will generally be
orientated at random
when no electric field
is applied.
An applied electric field will polarise the material by orientating the dipole moments of the polar
molecules.
dielectric
The molecules in a dielectric, when in an external electric field, tend to become oriented in a way that
reduces the external field.
(a)
(b)
(c)
(d)
Figure (a) shows the electric field when the space between the plates is empty.
When a dielectric material is placed inside the capacitor (b) it becomes polarised.
There is no net charge on the dielectric, but the charge is asymmetrically distributed (c).
r
r
This produces two electric fields (d) E0 outside the dielectric; and Eind inside the dielectric, which
r
r
r
r
opposes E0 . The net electric field is E  E0  Eind which is less than the electric field with no dielectric
present.




dielectric
In this first experiment, a capacitor is connected to a battery such that the voltage
remains constant. When a dielectric is inserted in the capacitor, the capacitance
increases and the charge on the plates also increases.
In this second experiment, the capacitor is charged and is then disconnected from the battery.
A dielectric is then inserted. In this case, the charge remains constant, but the dielectric increases
the capacitance and the potential across the capacitor drops.