Resonance (Part - 18)- Alternating Current, Physics Video Lecture - Class 12

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patterns part 18 is brought to you by
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please make sure that you have watched
all the videos and part 17 before going
ahead with part 18 so now we'll talk
about a very important phenomenon of
resonance related to LCR circuit because
this resonance is something which
actually puts LCR circuit into practical
uses I mean see there is no point in
studying anything which is just theory I
mean why are we studying LCR circuits by
adding even studying the alternating
currents that's because all these things
can be used in our practical purposes we
can implement them and we can make our
life simpler and easier so now till now
we just spoke about the theory of
alternating currents out what are
alternating currents how do alternating
currents affect a resistor and adapter a
capacitor three of them together so now
it is the time that we will slowly learn
concepts which are related to these
circuits or which are related to
whatever we studied so far and they are
equally useful in our day to day life so
resonance is one such very important
phenomena so what does the resonance it
is the tendency of a system to oscillate
at a greater amplitude at some
frequencies than at others so what is
resonance we will first try to
understand that so forth so as of now
you forget about alternating currents
LCR circuits AC circuits everything you
just concentrate on what is resonance it
means that a certain system will always
want to oscillate at some frequencies at
very high amplitudes
you understand what is oscillation right
it is like a pendulum moving like this
so this is known as oscillation what is
amplitude that means the maximum
displacement from the mean position so
this distance is your amplitude so there
may be a certain frequency is at which
the
amplitudes building more than at other
frequencies so that phenomenon is known
as the resonance for example you can
think it and you can relate it to real
life in this way that sometimes it
happens that every person likes to do
certain things more at certain times
like for example if it is your exam time
you feel like studying more so the
amount of study which you do in a normal
day is lesser than the amount of study
which you do during your exams time
right so that examination time is is a
push because of which you are your
amplitude is more if you are studying
more so if this kind of phenomenon is
known as resonance so it is formidable
systems that have a tendency to
oscillate at a particular frequency that
means the system this phenomenon of
resonance will occur for those systems
which have a tendency to oscillate at a
particular frequency and that frequency
is known as natural frequency so you
will understand it very clearly as soon
as I take this example before you let us
suppose that you have a pendulum you
have this pendulum this if you please
this pendulum on its own this pendulum
will oscillate with a particular
frequency right so it will have a
particular frequency oh that is called
natural frequency that means I am NOT
pushing the pendulum I am not shaking it
I am not doing anything I am just
leaving it on its own but it has some
natural frequency with which it will
oscillate now let us suppose if I come
back and if I start giving it a push
such that in the I mean I add up to the
natural frequency let us suppose the
natural frequency is that it should
oscillate like this 1 2 3 4 let us
suppose this is the natural frequency
and let us suppose I come and I give a
push to the Bob of the pendulum at the
same frequency that is 1 2 3 if I give
at the same frequency then what happens
the amplitude increases any
because of its natural frequency the
pendulum wanted to move this side now I
am also giving some push from this end
so it is moving all the more that is it
as amplitude is increasing all the more
so this phenomenon is known as resonance
so it is common among systems which have
by its own they have a natural frequency
that means they have a tendency to
oscillate at a particular frequency so
look at this example once again this is
your pendulum which is oscillating at
its natural frequency now if you come
from outside and give a push to the
pendulum in the same side its amplitude
increased right did you observe that the
amplitude increased now so this
frequency at which the pendulum
oscillates with a greater amplitude is
known as the resonance frequency that
means some external frequency adds up to
your natural frequency which results in
increase in amplitude right so in this
case the frequency of the push is equal
to the natural frequency and this is
known as the resonant frequency and this
is your resonance similarly you can also
take the example of a swing let us
suppose if you go to a children's pop
and you are sitting on the swing now you
swing on you're at your own pace that is
at your natural frequency now if I come
from behind and if I also start giving
you push at the same frequency whenever
you come back I push you again you come
back I push you that means I am also
pushing you at the same frequency with
which you are swinging so this push is
adding to the natural frequency of the
swing and the amplitude is increasing
therefore this is known as resonance and
this frequency is known as resonant
frequency so that means whenever I talk
of resonant frequency that means at
resonant frequency the amplitude will be
maximum right okay so now let us look at
the resonance of a series LCR circuit
what happens in
of an NCR circuit so when does resonance
occurs in case of a an NCR circuit what
did I tell you I told you that at
resonant frequency amplitude is maximum
that means whenever resonance occurs
that means the amplitude is maximum so
which amplitude am I talking about when
I am talking about an LCR circuit so in
an LCR circuit the amplitude I am
talking about is the current amplitude
so what is my current amplitude it is I
M which is given by V M divided by Z
right this would be the voltage
amplitude divided by the net impedance
of the circuit so that will be equal to
VM divided by root over R square plus XC
minus X L whole square right so this is
my current amplitude so if I say that I
want to see what happens at resonance
so at resonance my current amplitude
should be maximum now for amplitude
should be maximum that means at
resonance current amplitude should be
maximum now this current will be maximum
when the impedance will be minimum so
this implies that impedance should be
minimum now when what will be the
minimum value of this impedance
impedance will be minimum when X C is
equal to X L that means this entire term
will be equal to zero so impedance will
be minimum when X L minus X XC minus X L
whole square is equal to 0 that means
when XC is equal to XL right so this is
the condition where for resonance to
occur in a series LCR circuit now what
is XC it is 1 by Omega C what is X n it
is Omega L so from this we can say that
Omega is equal to 1 by root over L C so
this value of frequency is known as the
resonant frequency and we generally
denote
as Omega naught so Omega naught
represents the resonant frequency so now
if you look at it with the help of in
terms of this graph you see that the
value of the current amplitude increases
with the value of the angular frequency
Omega and it reaches a maximum value at
this maximum value corresponds to Omega
naught that is the resonant frequency
and then again decreases down so as
Omega keeps increasing the current
increases reaches a maximum value at
resonant frequency and again starts
falling down with increasing Omega so
this is how resonance occurs in case of
an LCR circuit and this resonance in LCR
circuit is used in many of our practical
purposes we will look at one of the very
good examples which many of us use in
our day to day life in the next slide so
one important point to be noted here is
that resonance is exhibited by a circuit
only if both L and C are present in the
circuit so if you take the example of
any if you consider any circuit which
has only inductor and resistor in that
case resonance cannot occur because
resonance can occur only when your
capacitive reactance and inductive
reactance are equal and opposite to each
other and therefore they cancel out each
other so it is a must that you should
have a capacitor and inductor both
present in an LCR circuit if you want to
have or if you want to experience the
phenomenon of resonance so resonance is
not possible without both L and C
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