Energy Stored in Capacitors; Energy density - Capacitor & Capacitance, Physics, Class 12 Video Lecture - Class 12 | Best Video for Class 12

hello friends this video on capacitance
and capacitance part 19 is brought to
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please make sure that you have watched
all the videos in part 18 before going
ahead with part 19 now we will talk
about energy stored in a capacitor we
have already seen that capacitor stores
charges so what do you think will let me
pass it or store some attention as well
in this way from where is the charge is
coming to the capacitor it is coming
from some source some source which we
are considering in most of the cases now
as battery so let us suppose there is a
battery which is supplying charges to
the capacitor to the first plate of the
capacitor some positive charges are
coming okay and then the negative
charges are getting induced on the other
plate of the capacitor so imagine the
situation like this that the battery is
doing nothing but taking some electrons
from the first plate and giving them to
the second T and that is how the second
place is getting amused with negative
charges so that means the battery is
doing some work transfer this negative
charges or transfer these electrons from
the first flip to the second plane like
all we can say it in this way that there
is some work done in pulling positive
charges from the second plate to the
third second flake in the first place I
mean both are the same things like
taking positive charges from the first
eight and leaving it to the same
template or picking negative charges
from the second click will give you the
first pick both are the same things
right so what this work done is
basically stored as click to static
energy in piece of a capacitor so the
work done in transferring charge from
negative towards positive flake is
stored as electrostatic energy in
capacitor so when I talk about
transferring charge from the positive
plate to the negative plate we are
transferring electrons then I talk about
transferring positive charge then we are
transferring it from there maybe
plain to the positive people so let us
take help of the diagram so that it
becomes easier for you to understand
this this your capacitor with two plates
of the capacitor and this was the
electric field is established between
them now when I talked about a battery
source which is supplying electrons
later suppose this is my positive plate
and this is my negatively okay keep
electrons some work is done to take
electrons from this positive plate and
send it there since electrons are coming
to this plate that is why this place is
getting negatively charged so there is
some work done in bringing electrons
from positively negatively so electrons
from positive plate - negative click all
in other words we can say bring positive
charges from negative plate to
positively both we mean the same thing
right either I take the work then you
take in an electron from positive to
negative plate is equal to the work done
in taking a positive charge from
negative to positive plate right so this
is how we do this work then is basically
stored as electrostatic energy in
capacitor so please understand this so
this energy stored as electrostatic
energy U is of a capacitor right so how
do we know I mean when does this energy
get stored the energy is basically
stored giving charging when the
capacitor gets charged that is the
static way to a voltage source the
voltage source will supply some amount
of charge to the capacitor and the
capacitor will gets charged so during
this charging phase the capacitor will
store the electrostatic energy in itself
now when it gets charged it has
electrostatic energy with it now when
again during discharging this has to
supply energy then it will deliver the
same energy in the form of power to the
circuit so there is no dissipation of
energy as such there is more
lost asset whatever energy the capacitor
beams during charging if stores with it
and again it delivers the same energy in
the form of power to the entire circuit
so that is all about the electrostatic
energy stored in a capacitor now how do
you how do we calculate the
electrostatic energy spoon in the
capacitor so for that we need to have a
mathematical expression so now let us
concentrate on that expression now a
capacitor always gets charged gradually
so since it gets charged gradually let
us assume that at any stage at any stage
of charging let us say that the charge
on the capacitor is equal to Q so what
would be the potential on the capacitor
potential little denoted by V that will
be equal to Q divided by C where C is
the capacitance now let us suppose there
is a small amount of work done say which
is denoted by DW in giving an additional
charge DQ that means in leaving
additional charge DQ - the capacitor
during charging the voltage source is
supplying charges to the capacitor right
and those charges are then getting
carried from one clip to another so let
us suppose in giving charge D - the
amount of work which is done is BW okay
so how will you write DW what can we
write DW DW is nothing but DQ into the
potential right that is how we define
work and work done is nothing but you
remember I told you in our previous
lesson on electrostatic potential that
work done is nothing but the potential
difference between two points so well
then per unit charge is defined as
potential right so well then will be
equal to the charge into the
electrostatic potential so now this
potential D can be written as q by C
therefore the total work done will be
Quenton integration of DW that is
integration of Q by C into D Q so this
will be equal to 1 by C integration of Q
P Q where Q varies from 0 to capital Q
by capital Q is the total charge on the
capacitor fleet so this becomes 1 by C Q
square by 2 from 0 to Q so this becomes
1 by C Q square by 2
therefore the energy which is stored in
the capacitance this work then is
nothing but it is told as electrostatic
energy which is denoted by u so this U
is equal to 1 by 2 Q square by C now you
can write the expression for
electrostatic energy in terms of Q C in
terms of Q V in terms of CV because they
are all related to each other so this is
the expression for electrostatic energy
in a capacitor now since we know that Q
is equal to C into V so you can also
replace Q with C V so you will get it as
half in DC means well so they are all
different forms of expressing the same
thing so did you understand the concept
of energy which is stored in capacitor
now let us talk about energy density so
once you have understood waters that
energy is stored in a capacitor energy
density is quite simple it is nothing
but energy stored per unit volume of
space so energy density is generally
denoted by small U energy we denote
energy with capital u and energy density
with small U so we will find out an
expression for energy density energy
density U is energy stored per unit
volume so what is energy stored in
capital u and volume is nothing but area
of the plates into the distance between
them because that because energy is
stored in the electric field region that
right this is these are the two plates
of the capacitor here you have electric
field so the energy is basically stored
in this region right so what could be
the volume of this region
you consider the beliefs of the
capacitor multiplied by the distance
between them so this U is nothing but
half CV square this into 1 by E into D
now we also know that capacitance for a
parallel plate capacitor is given by ay
epsilon not writing do B Square divided
by a into D so a and K will get
cancelled so you get half epsilon not B
by D whole square right this is the end
is T now what is V by D you remember
gradient of potential is nothing but
electric field so this is v square
therefore energy density U is given by
half epsilon knot e square so this is
all about the energy which is stored in
a capacitor now we will again look at
some problems based on this energy
stored in a capacitor thank you please
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