LC oscillations (Part - 25) - Alternating Current, Physics Video Lecture - Class 12

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the power 24 before going ahead with
part 25 we will now talk about an
interesting phenomenon that happens with
LC circuit that means a circuit where we
have an inductive and a capacitor
connected in the same circuit so we will
see water LC oscillations and what give
rise to such oscillations what happens
is let us suppose you if you have a
circuit with a capacitor and an inductor
as you can see here the energy which is
taken from the cell by this capacitor to
charge itself that energy keeps
oscillating between this capacitor and
this inductor so the energy is
oscillating between them and these
oscillations between L and C is referred
as LC oscillations so we will talk about
the pattern of the oscillations in
detail in the next slide so here we will
see what gives rise to this oscillation
I mean what causes this energy to get
transferred from the capacitor to the
inductor back to the capacitor again to
the inductor and back to the capacitor
and so on what happens is when the
capacitor is given some energy from a
cell it first of all it charges itself
right that is a general phenomenon which
used to happen even in your decent
circuits whenever you switch on the
circuit first of all the capacitor will
take some charge it will charge itself
once it is completely charged in case of
DC current it will not allow further
current or for the charge to come to it
that is it will block the DC current but
when we are talking about AC current I
mean let forget that an inductor is
connected to the circuit if we talk only
about the capacitor what happens when we
give when they apply AC voltage to it
like a fast eater will first charge
itself it will again discharge itself
charge itself so it will organically
charge and discharge itself because the
alternating voltage which is being
supplied to the capacitor is also
changing its direction alternating right
now in this case we are connecting
another inductor to this capacitor so
what happens initially the capacitor
takes all the energy from the cell and
charges itself so let us suppose that
the capacitor is charged to some charge
- so after when the capacitor is fully
charged it starts discharging to this
inductor which is connected to it now as
soon as this discharging happens that is
there is some current which starts
flowing through the circuit so there is
a change in magnetic flux in the circuit
you remember Faraday Lenz law so
whenever there is a change which is
taking place so that means still now the
capacitor was getting charged now the
capacitor starts discharging so that
means the system or the circuit is
experiencing a change so because of this
change in current there would be a
change in magnetic flux now this change
in magnetic flux would be experienced by
this inductor so due to this change in
magnetic flux there will be an EMF which
will be induced in this inductor so what
will be that EMF let us say that EMF is
e so this is the self induced EMF in
this inductor so this EMF will be given
by minus L di by DT that is what we
studied in self induction and what is
this negative sign form remember Lenz
law negative sign sees that the self
induced EMF will try to oppose the
change which produced it so what is the
change that produced it the charging of
the capacitor at the discharging of the
capacitor so that means when the current
was flowing through this this change in
current resulted in a self induced EMF
in this inductor so this self induced
EMF will try to oppose the growth of
this current it will
want this tunnel to grow as I desire
what will happen as soon as that
capacitor gets completely discharged all
the energy that was stored in the
capacitor here will now be stored in the
inductor so when the energy was stored
in the capacitor how was it stored as we
discussed in our lesson on capacitance
you remember right so between the plates
of the capacitor the energy is stored in
the form of electric field energy and
what is that energy that energy is
nothing but half Q square by C so this
is the energy stored by the capacitor
right where Q is the charge on the
capacitor and C is the capacitance so
when the capacitor was initially charged
from the cell it had this much of energy
so it had the total energy now as soon
as it started discharging the energy of
the capacitor kept decreasing and the
energy stored by the inductor kept
increasing so what does the energy
stored by the inductor remember the
lesson on inductance in your magnetism
chapter there we saw that the work done
by an inductor against the back EMF that
the self induced EMF or the back EMF
whatever you call it what it what is the
work done that is half Li square where I
is the current induced in the inductor
and L is the self inductance of the
inductor so this is the energy stored in
the inductor so that means in this
circuit what is happening is initially
when the capacitor is fully charged it
has this much of energy that is the
total energy is kept by the capacitor
then the capacitor starts discharging to
the inductor now since that inductor
experiences a change in flux there is an
induced EMF in the inductor which
opposes the growth of current since the
inductor opposes the growth of current
so it all the more supports the
discharging of the capacitor so
capacitor keeps on discharging and
finally the capacitor is completely
discharged so when the capacitor is
completely discharged that means there
is no charge stored in the capacitor
that means there is no energy stored in
the capacitor so at that point of time
all the energy is stored by the inductor
as magnetic field energy that is as this
energy half Li square now what happens
when the inductor is storing all the
energy again this inductor will start
charging the capacitor so the capacitor
will start charging again therefore as
soon as the capacitor starts charging up
the energy stored in the capacitor again
starts increasing at the cost of the
energy which was stored in the inductor
so that means this cycle keeps going
continuously as long as there is some
external resistance present in the
circuit
otherwise they said this phenomenon will
keep continuing that the energy stored
in the capacitor will get transferred to
the energy stored by the inductor and
vice-versa and so on so these
oscillations are therefore as LC
oscillations so LC oscillation is
basically the oscillation of the energy
taken from the cell between the
capacitor and the inductor so we can see
that here basically the electric field
energy and the magnetic field energy
keeps oscillating so when electric field
energy is maximum it decreases gradually
and the magnetic field in energy
increases again the magnetic field
energy reaches its maximum when the
electric field energy 0 again it starts
decreasing and increases the electric
field energy and this process continues
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