CAPACITORS
Symbols:
dielectric
A
capacitor
is
an
electronic
device
designed
to
store
charge.
A
capacitor
consists
of
two
oppositely
charged
plates.
A
nega=ve
charge
is
removed
from
one
plate
and
placed
onto
the
other,
leaving
one
side
with
a
nega=ve
charge
and
the
other
side
with
a
posi=ve
charge.
The
plates
are
usually
separated
by
an
insula=ng
material,
called
the
dielectric.
ABer
the
plates
have
aCained
their
charge,
the
NET
charge
of
the
capacitor
as
a
whole
remains
equal
to
zero.
The
charge
on
the
capacitor
is
propor=onal
to
the
POTENTIAL
DIFFERENCE,
V,
across
the
plates.
In
prac=ce,
this
voltage
or
poten=al
difference
would
be
obtained
by
hooking
the
plates
of
a
capacitor
to
the
terminals
of
a
baCery.
Q = CVab
note
the
E
field
lines
from
the
plates.
The
dielectric
actually
LOWERS
the
E
strength
(and
thus
V)
across
the
plates.
At
constant
Q.
the
dielectric
must
therefore
INCREASE
the
capacitance
value
of
the
capacitor!
Recall,
we
can
get
the
strength
of
the
electric
field,
E,
as
the
ra=o
of
voltage
and
distance
of
charge
separa=on:
V
E =
d
1
F
=
1
Coulomb/Volt
The
“C”
in
the
equa=on
above
is
a
propor=onality
constant
called
the
CAPACITANCE.
The
capacitance
of
a
capacitor
is
usually
expressed
in
units
called
farads
(an
abbreviated
version
of
Michael
Faraday’s
name).
The
capacitance
is
a
func=on
of
the
type
of
dielectric.
the
surface
area
of
the
plates,
and
the
distance
between
the
plates:
ε
has
units
of
F/m
C=
KεoA
εA
or C =
d
d
K
is
the
dielectric
constant
and
εo
is
the
vacuum
permiYvity
ε
is
known
as
the
permi&vity
of
the
dielectric.
This
value
is
rela=ve
to
a
vacuum
dielectric
(ε/εo
=
1)
and
reflects
the
ability
of
the
dielectric
to
store
electrical
energy
in
an
electric
field.
The
dielectric
INCREASES
the
capacitance
rela=ve
to
a
vacuum.
K>1
Supplemental
informa=on
about
dielectric
materials
What
K
means
for
a
dielectric
material.
K
is
the
factor
by
which
a
dielectric
reduces
the
voltage
across
the
plates
of
a
capacitor
(or
increases
the
capacitance
C)
compared
to
a
vacuum.
For
constant
Q,
we
find
that
an
insulator
inserted
between
the
plates
of
a
capacitor
reduces
the
voltage
from
Vo
to
Vd.
For
the
capacitance
equa=on
below
to
remain
in
balance,
(+)
plate
Q = CV
C
must
INCREASE
to
Cd
in
propor=on
to
the
amount
that
Vo
decreases
to
Vd
.
We
can
define
K
as
the
ra=o
of
C
or
V.
In
any
case,
K
>
1.
K =
Cd
V
or K = o
Co
Vd
The
dielectric
polarizes,
thus
aligning
its
charges
with
the
charged
plates.
This
effec=vely
reduces
E
and
V
across
the
plates.
(‐)
plate
ANALYZING
A
CIRCUIT
WITH
CAPACITORS
We’ll
just
look
at
some
very
basic
rela=onships
here
but
expand
them
in
the
CIRCUITS
unit.
PARALLEL
vs
SERIES
a
circuit
is
a
closed
loop
that
allows
electrons
to
flow
from
a
high
poten=al
(voltage)
to
a
low
poten=al
(voltage).
Generally,
for
the
purposes
of
analyzing
a
circuit,
the
(+)
end
of
a
baCery
is
set
as
the
high
V
terminal,
and
the
(‐)
end
as
the
0
V
terminal.
if
capacitors
(or
anything
else)
are
on
two
or
more
“loops”
in
a
circuit
they
are
said
to
be
in
PARALLEL.
If
they
are
on
the
SAME
loop,
they
are
said
to
be
in
SERIES.
A
branch
point
in
a
circuit
creates
a
loop.
branch
point
⎛ 1
1⎞
SERIES
arrangement
and
Ceq = ⎜ + ⎟
⎝ C1 C2 ⎠
the
equivalent
capacitor
−1
PARALLEL
arrangement
and
the
equivalent
capacitor
Ceq = C1 + C2
NOTE:
capacitors
in
series
yield
a
LOWER
capacitance
than
any
one
of
the
capacitors
in
series
Voltage
drop
across
capacitors
in
series
Considering
the
circuits
above,
let’s
say
that
point
“a”
is
the
high
V
end
of
the
circuit
and
that
Va
=
12
.
At
point
“b”,
V
=
0.
The
voltage
drop
across
C1
and
C2
(or
Ceq
in
the
circuit
to
the
right)
will
be
12
volts.
The
voltage
drop
across
each
capacitor
MUST
add
up
to
the
total
poten=al
difference
(voltage
drop)
of
V
=
12.
Note that the charge Q on each capacitor in series is the same.
Across
C1
,
the
voltage
drop
ΔVac
=
Q/C1
Across
C2,
the
voltage
drop
ΔVcb
=
Q/C2
ΔVab
=
ΔVac
+
ΔVcb
Note:
If
the
capacitors
are
different,
the
voltage
will
divide
itself
such
that
smaller
capacitors
get
more
of
the
voltage!
This
is
because
they
all
get
the
same
charging
current,
and
voltage
is
inversely
propor=onal
to
capacitance.
Voltage
drop
across
capacitors
in
parallel
If
the
capacitors
are
in
parallel,
like
the
diagram
to
the
above
leB,
the
voltage
drop
is
the
same
across
each.
For
example,
if
Va
=
12
and
the
Vb
=
0,
then
both
C1
and
C2
experience
a
voltage
drop
of
12
V.
A
notable
difference
from
the
series
circuit
is
that
the
charge
on
the
capacitors
may
be
different
in
a
parallel
circuit.
The
total
charge
Qtotal
=
Q1
+
Q2