Download Capacitor Basics File

The Capacitor
Capacitors
and
capacitance
The capacitor is a useful device
for storing electrical energy
(“storing charge”).
Ewald Georg von Kleist, a German
scientist invented the capacitor in
November 1745.
Several months later Pieter van
Musschenbroek, a Dutch professor
at the University of Leyden came
up with a very similar device in the
form of the Leyden jar, which is
typically credited as the first
capacitor.
The Leyden jar consisted of a
glass jar, half filled with water and
lined inside and out with metal
foil.
The Capacitor
The Capacitor
The capacitor is a
useful device for storing
electrical energy
(“storing charge”).
It comprises two
conducting plates in
close proximity to each
other.
Real capacitors
How does it fit?
Let’s Take one apart!
The Capacitor
A practical capacitor consists of two
flexible conducting strips separated
by an insulating layer rolled in a
cylindrical tube
The strips are like the metal plates of
the parallel plate capacitor but they
are much smaller in physical size.
The maximum working voltage of a
capacitor should never be exceeded.
The Capacitor
When the capacitor is connected to a battery, equal and opposite
charge flows onto the plates
The current flows until the potential difference between them is
the same as the battery’s e.m.f.
V = e.m.f
-q
+q
The Capacitor
When you connect a capacitor to a
battery, here's what happens:
• The plate on the capacitor that is
attached to the negative terminal of
the battery accepts electrons that the
battery is producing.
• The plate on the capacitor that is
attached to the positive terminal of
the battery loses electrons to the
battery.
Once it's charged, the capacitor has
the same voltage as the battery (1.5
volts on the battery means 1.5 volts
on the capacitor).
The Capacitor – water tower analogy
When the capacitor is
connected to a battery,
charge flows onto the
plates until the p.d.
between them is the same
as the battery e.m.f.
A capacitor stores energy.
Often said to store
charge.
Using water analogy, a
capacitor is similar to a
water tower which stores
water energy produced by
a water pump.
Capacitor versus battery
When a capacitor is charged, it stores
electrical energy
When a battery is charged it converts
electrical energy from a charger into
chemical energy and stores chemical
energy.
Battery usually stores much more
energy than a capacitor, but energy
from a battery cannot be released fast.
The Capacitor – applications
Therefore we should use a capacitor when
we need a fast release of relatively small
amount of energy, while a battery is useful if
we need more energy which is slowly
released.
Sometimes, capacitors are used to store
charge for high-speed use. That's what a
flash does. Big lasers use this technique as
well to get very bright, instantaneous flashes.
Capacitors can also eliminate ripples. If a line
carrying DC voltage has ripples or spikes in it,
a big capacitor can even out the voltage by
absorbing the peaks and filling in the valleys.
A capacitor can block DC voltage.
The Capacitor
The capacitor is a useful
device for storing electrical
energy (“storing charge”).
It comprises two
conducting plates in close
proximity to each other.
When the capacitor is
connected to a battery,
equal and opposite charge
flows onto the plates until
the potential difference
between them is the same
as the battery e.m.f.
A capacitor stores
energy.
Often said to store
charge.
Dielectrics
In order to increase the amount
of stored charge in a capacitor,
a dielectric can be added
between capacitor plates.
An insulating material
(dielectric) contains atoms
with bound electrons.
A positive charge attracts these
electrons to one side of the
atom, a negative charge repels
them from the other, creating a
dipole.
Dielectrics
A positive charge attracts these electrons
to one side of the atom, a negative charge
repels them from the other - creates a
dipole.
No charge, no electric field on a capacitor
plate. Dipoles have random orientation.
When some charge is stored on a
capacitor, the electric field appears.
Positive charges of dipoles are attracted to
the negatively charged capacitor plate,
while negative charges of dipoles are
attracted to the positive capacitor plate.
Therefore, dipoles orient along field lines.
Dielectrics
The net effect is to reduce the effective surface charge on the plates, and so
the capacitance increases, since the same charge on the capacitor plates
produces weaker electric fields.
In other words, oriented dipoles create the electric field pointed in the
opposite direction with respect to the applied field (electric field created by
the capacitor plate).
-q - Charge induced
by oriented dipoles
Q - Charge
on capacitor
plates
The capacitor
“feels”
smaller
charge Q-q
Dielectrics
Field generated by capacitor
plate E
“Field” or polarization of
dielectric P = 0 cr E where
coefficient cr is called
susceptibility, 0 permittivity
of a vacuum
The total field from capacitor
plate and dielectric is related
to 0 (1+cr) E or r0 E with
the electric permitivity of a
dielectric r =1+cr
Therefore, the electrical
permitivity of a vacuum is 0
and the permitivity of a
dielectric is r0.
Dielectrics reduce
the effective charge
on a capacitor plate
and so increase
capacitance.
Dielectrics
An insulating material
(dielectric) contains atoms with
bound electrons.
A positive charge attracts these
electrons to one side of the
atom, a negative charge repels
them from the other - creates a
dipole.
The net effect is to reduce the
effective surface charge on the
plates, and so the capacitance
increases.
The electrical permittivity of a
vacuum is 0 and the
permittivity of a dielectric is r0.
Dielectrics reduce
the effective charge
on a capacitor plate
and so increase
capacitance.
Charging a Capacitor
A capacitor is charged through a
resistance. The larger the
resistance, the longer it takes to
charge.
As charge flows onto the plates,
a potential difference appears
between the plates.
Any relations between Q and V ?
V
-Q
e-
+Q
e-
R1
R2>R1
Charging a Capacitor – water
V
analogy
Yes, the stored charge is
proportional to the voltage
difference between capacitor
plates.
Water tank analogy: capacity or
volume of a water reservoir is
analogous to the capacitance of a
capacitor.
The value of capacitance is
defined as the amount of charge
on each plate when it has
reached the battery e.m.f.
divided by that e.m.f.
C
Q
V
C is measured in farads.
-Q
e-
+Q
e-
Charging a Capacitor –
capacitance in farads
1 farad is the capacitance of a
capacitor which can store 1
coulomb if a voltage of 1 Volt is
applied to its plates.
A 1 farad capacitor can store 6.25
x 1018, or 6.25 billion billion
electrons if 1 volt is applied.
One amp represents a rate of
electron flow of 1 coulomb of
electrons per second, so a 1 farad
capacitor can hold 1 amp current
during 1 second at 1 volt.
A 1-farad capacitor would typically
be pretty big: the planet Earth:
about 710 μF. For this reason,
capacitors are typically measured
in microfarads.
Q
C
V
Q=+1C
=1V
Q=-1C
710 μF
Farad: battery versus capacitor
A standard alkaline AA battery holds about
2.8 amp-hours.
That means that a AA battery can produce
2.8 amps for an hour at 1.5 volts (about 4.2
watt-hours – a AA battery can light a 4-watt
bulb for a little more than an hour).
To store one AA battery's energy in a
capacitor at 1 volt, you would need 3,600 s x
2.8 amps / 1 Volt = 10,080 Farads to hold it,
because an amp-hour is 3,600 amp-seconds.
10,080 Farads is going to take up a LOT
more space than a single AA battery!
Obviously, it's impractical to use capacitors
to store any significant amount of power.
Charging a Capacitor
Charged through a resistance.
The larger the resistance, the
longer it takes to charge.
As charge flows onto the plates,
a potential difference appears
between the plates.
The value of capacitance is
defined as the amount of charge
on each plate when it has
reached the battery e.m.f.
divided by that e.m.f.
Q
C
V
C is measured in Farads.
C is the symbol for
capacitance
C=Q/V
Unit is the Farad (F)
Parallel Plate Capacitor
Consider two parallel metal plates of the same area.
Larger area plates means more
charge can be stored on each.
Closer together plates give stronger
attraction between the opposite
charges, so more charge can be
stored.
Parallel Plate Capacitor
Consider two parallel metal plates of the same area.
Larger area plates means more
charge can be stored on each.
Closer together plates give stronger
attraction between the opposite
charges, so more charge can be
stored.
𝐶 ∝
𝐴
𝑑
seems reasonable?
Parallel Plate Capacitor
Consider two parallel metal plates of the
same area.
The larger dielectric constant of
the material in between the more
charge can be stored.
It can be shown that:
 0 r A
C
d
Parallel Plate Capacitor
Relative permittivity
No units
1 for air or vacuum
Permittivity of
Free Space.
(Constant).
ε0 Value is given on
formula sheet
ε0 =8.85 * 10
-12
Fm
-1
C
 0 r A
d
Parallel Plate Capacitor
1.
2.
3.
4.
5.
A capacitor comprises two discs of metal 20 cm in
diameter that are 0.5 mm apart. It’s filled by
polythene (r=2.3) between plates. The permittivity
of free space 0=8.85x10-12 Fm-1.
Calculate capacitance of the capacitor and the
charge on each plate when connected to a 1.5 V
battery. How long can this capacitor keep 2.0 A
current?
The diameter is 0.2m, the distance between plates is
5x10-4m.
The areas of plates are A=pd2/4 =
3.14x0.22/4=3.14x10-2 m2.
C=8.85x10-12x2.3x3.14x10-2/(5x10-4) [Fxm-1xm2/m]
= 13x10(-12-2-(-4))[Fm(-1+2-1)]= 13x10-10[F]=1.3x10-9 F.
To find the charge we use Q=CV=1.3x10-9F x 1.5V =
2.0x10-9C.
I=Q/t, thus, t=Q/I = 2.0x10-9C/2.0A = 10-9s = 1ns
10-9 nano
n
Parallel Plate Capacitor
Consider two parallel metal plates of the same area.
Larger area of the plates
means more charge can
be stored on each.
Closer together plates
give stronger attraction
between opposite
charges, so more charge
can be stored.
The larger the dielectric
constant of the material in
between, the more charge
can be stored.
It can be shown that:
 0 r A
C
d
The capacitance
of a parallel plate
capacitor is
C=A0 r/d