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Memorex CP8 TURBO UNIVERSAL REMOTE CONTROL Instrukcja Użytkownika Strona 71

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THE
MATH
OF
CAPACITORS
By
Louis
E.
Frenzel
You
can't
design
with
capacitors
unless
you
know
exactly
what
they
are
capable
of
in
mathematical
terms.
Here's
the
chance
to
learn
what
you
need
before
you'll
need
it
HE
CAPACITOR
IS
SUCH
A
COMMON
ELECTRONIC
COM-
ponent
that
its
importance
is
usually
understated.
Further,
its
function
is
pretty
well
understood.
It
stores
electrical
energy
in
the
form
of
an
electric
field
created
by
a
charge
of
opposite
polarities
on plates
across
an
insulator.
The
charging
and
discharging
of
a
capacitor
produces
many
useful
effects.
Capacitors
are
commonly
used
in
timing,
sequencing
and
delay
operations.
Capacitors
are
also
widely
used
as
filters
and
phase
shifters.
Capacitors
offer
an
opposi-
tion
to
current
flow
called
capacitive
reactance.
And
when
combined
with
inductors,
capacitors
produce
that
invaluable
phenomenon
known
as
resonance.
In
this
installment,
we
take
an
in
-depth
look
at
capacitor
operation
and
application
by
way
of the
math
that
defines
and
describes
it.
Capacitor
Review
Capacitors
are pretty
well
known
to
most
of
you,
so I
won't
belabor
you
with
the
obvious.
But
just
for
openers,
here's
a
quickie
overview
of
capacitor
operation.
It
should
refresh
your
memory
about
basic
capacitor
operation
and
charac-
teristics.
First.
a capacitor
is
nothing
more
than
two
conductors
separated
by
an
insulator.
The
two
conductors
are
usually
called
plates,
while
the
insulator
is
referred
to
as
the
di-
electric.
A
simple
capacitor
is
illustrated
in
Fig.
I.
The
dielectric
can
be
any
insulator,
but
common
ones
are
ce-
ramic,
mica,
paper.
and
various
plastics
such
as
polystyrene.
Air
or
free
space
is also
a common
dielectric.
The
symbol
used
to
represent
capacitors
in
schematic
diagrams
is
also
shown
in
Fig.
I.
When
a
capacitor
is
connected
to
a
voltage
source,
it
becomes
charged.
That
is,
one
plate
takes
on
a
negative
charge
and
the
other
a positive
charge.
Figure
2
shows
what
happens
when
a
battery
is
connected
to
a capacitor.
The
positive
terminal
of
the
battery
pulls
many
electrons
from
plate
A.
The
negative
terminal
of
the
battery
deposits
extra
electrons
on plate
B.
The
capacitor
is
then
said
to
be
charged.
The
dielectric
prevents
electrons
from
flowing
between
plates
A and
B.
The
capacitor
blocks
the
flow
of
direct
current.
With
the
capacitor
charged,
the
positive
and
ncgatke
nc L.apaa.uwI
will
Keep on cnarging
until the full 12
volts
appears
across it. It takes about
five time constants for the
full
charge to be reached. In the example
above, it
will
take
5
x
.47
= 2.35
seconds
for the
capacitor to fully charge to
approximately 12
volts.
The curve in
Fig. 6 shows the
voltage on the capacitor
with
respect to time.
The one and
five time -constant
points are
identified there.
Actually
it would be nice to know the exact
voltage
on the
capacitor at
any given time during
the charging process. If
we
knew the mathematical equation
representing the curve
in
charges
on
the
plates
attract
one
another
across
the
dielectric.
Remember,
opposite
charges
attract,
like
charges
repel.
That
attraction
sets
up
an
electric
force
field
between
the
plates.
If
the
battery
were
removed,
the
charge
would
remain
due
to
the
mutual
attraction.
The
capacitor
stores
electrical
energy
in
the
form
of
an
electric
field.
Now
if
we
short
the plates
of
the
charged
capacitor
as
in
Fig.
3.
the
electrons
on
plate
B
will
rush
through
the
short
to
neutralize
the
positive
charge.
That
sudden
momentary
rush
of
current
discharges
the
capacitor.
The
charge
on
the
capacitor
is
measured
in
Coulombs.
A
coulomb
is
a quantity
of
electrons.
One
coulomb
is
6.28
x
1018
electrons.
That
is
a
big
bunch
of electrons.
If
that
number
of
excess
electrons
appears
on
one
plate
to
make
it
negative.
then
an
exactly
equal
number
of
electrons
will
be
removed
from
the
other
plate
to
make
it positive.
Knowing
the
charge
in coulombs
(Q)
and
the
voltage
(V)
that
produces
it, gives
us
a
way
to
state
the
size
or
capaci-
8
7
6
5
4
3
2
1
o
METAL
PLATES
DIELECTRIC
(INSULATOR)
Fig.
1 -This
is a
standard
parallel
-plate
capacitor.
Many
capacitors.
such
as
axial
and
radial
types.
do
not
have
flat
plates.
but
operate
on
the
same
principles.
- - - - 63.2%
2 3 5
(TI
TIME
CONSTANTS
Fig. 6-The
capacitor charges quickly
at
first.
but
then the
build
up of further charge
takes
longer and
longer.
81
79
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