AC inductive circuit - Alternating Current Video Lecture - Class 12

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make sure that you have watched all the
videos ten past seven before going ahead
with part eight so let us now talk about
inductive circuit so we will talk about
such an AC circuit where the only
circuit element that will be present is
an inductor so you will not have
resistor anymore even if the resistor
will get replaced you can end up that
and we will study the same things for an
inductor that is how much is the current
that will flow through the circuit if we
apply an alternating voltage to it what
is the voltage cut into relationship how
do we represent the voltage current
relationship graphically as well as with
a phasor diagram and what is the power
associated with an inductor so these are
the few things which we talked about
during discussing resistive circuits so
we will now talk about all the same
things in inductive DC circuit so first
let us start with what happens when an
AC voltage is applied to an inductor so
in this case what is my source voltage
that is what is the voltage which we
have applied that voltage is nothing but
your normal alternating voltage which is
represented as V is equal to VM sine
Omega T so we will see that when we
apply a voltage V what would be the
current that will get generated in this
inductive circuit so here also we will
apply Kirchhoff's loop rule so again
according to Kirchhoff's loop rule the
sum of all the EMFs the net EMF of the
circuit should be equal to the sum of
the product of the current and the
retrospective resistances so in this
circuit do you see any resistance there
is no resistance at all
right so no resistors in the circuit so
since there are no resistors there is
one EMF that is this voltage source that
is one EMF
and the other EMF is the induced EMF in
this coil let us suppose this inductor
is of inductance L so we have this
inductor which is of inductance L what
will happen as soon as current flows
through the circuit or whenever since it
is an alternating current so the current
will keep changing so when the current
changes the flux or the magnetic flux
associated with the current also changes
and you remember electromagnetic
induction right we talked about Faraday
Lenz law what did that say that say that
whenever there is a change in flux a
current is induced or an EMF is induced
in the inductor so therefore there will
be a self induced EMF on this inductor
which will try to oppose the change
which caused it right you remember all
those concepts or you remember all those
laws of lens and Faraday right so there
will be one EMF left one is the source
EMF that is the source voltage and there
will be another self induced EMF so that
means there are two EMF in the circuit
one is the source voltage and the other
one is the self induced EMF let me call
the self induced EMF as e so this will
be equal to since there are no resistor
so this will be equal to zero so what is
this e this e is the self induced EMF in
that inductor that is L right so we can
write it as V and what is self induced
EMF in our previous lesson we studied
that self induced EMF is equal to minus
L di by DT so we can write the same
thing here that is L di by DT is equal
to zero so now we can replace V with VM
sine Omega T right so this minus L di by
DT is equal to zero so now this can be
written as VM sine Omega T is equal to L
di by DT so
can write it as VM sine Omega T DT
divided by L is equal to di because our
aim here is to calculate or to evaluate
or to determine the value of current
which will be flowing through the
circuit that means we have to determine
the value of I so this we can now we can
integrate it on both sides because on
integrating we will get the value of I
so this we will integrate from some
value 0 to I so we can write it as I is
equal to VM divided by L integration of
sine Omega T DT so this can be written
as VM divided by L minus cos Omega T
divided by Omega write this plus some
constant because during integration you
get an integration constant so therefore
we can write as I is equal to minus VM
divided by Omega L into cos Omega T plus
some constant now what could be the
value of this integration constant now
since we know that the source EMF or the
source voltage oscillates symmetrically
about zero how do we know that because
we know that our source voltage is V
which is equal to VM sine Omega T so
this source voltage oscillates between
plus VM and minus VM write this value
oscillates between these two maximum and
minimum values now since it oscillates
symmetrically about zero because both
sides above zero for example if this is
your this is how your source voltage
looks like so this is your zero so it
oscillates symmetrically about zero it
goes to plus VM again it goes to minus
VM it goes to plus BM minus VM so it is
oscillating symmetrically about zero
therefore the current should also
oscillate about zero so current should
also oscillate about zero and that is
why we do not want
integration constant so this integration
constant should also be zero because if
we want that it is oscillating about 0
that means there should be no
integration constant here because if you
have some term here that means it is not
oscillating about 0 instead it is
oscillating about that value right so
therefore we say that I is equal to
minus VM divided by Omega L into cos
Omega T so now what we do we replace VM
by Omega L with I M right like how in
that case in case of resistive circuit I
n was equal to VM by I so here it is VM
by Omega L so now this we can write it
as I is equal to minus I M cos Omega T
now how did I represent my a source
voltage this is how I represented my
source voltage that is in terms of sine
Omega T so we will represent current
also in terms of sine function so that
it becomes easier for us to find out the
phase difference act between them so let
us write it as I M into minus cos Omega
t minus cos Omega T can be written as
sine of Omega t minus PI by 2 because
you know that sine 90 minus theta is
equal to cos theta here we have minus
cos theta so we have made it as sine
theta minus PI by 2 right so this is the
current which will flow through an
inductive circuit so this was my input
not input in the sense that this was the
voltage which was applied to the circuit
and this was the current which will flow
through the circuit so what do we see
from here we see that this time current
and voltage are not in phase they would
have been phase if both had sine Omega T
but here we see that for the expression
of current it has sine Omega t minus PI
by 2 that means they are out of phase by
PI by 2 right so we will talk about that
in
till when we represent the phase
relationship between voltage and current
graphically as well as with the help of
phasor diagrams that time we will talk
about it in detail so for now we will
see that we then now focus on the
current amplitude because here the
current amplitude was little different I
mean in case of resistors we took it as
I am is equal to VN by r so here it is
VM by Omega L so we will now focus on
this current amplitude so while when we
study about current amplitude we will
see that there is a new term which has
come into picture so let us look at the
current amplitude which we found here so
we saw that the current amplitude that
is I M is equal to VM divided by Omega L
now if you compare this with I is equal
to V by r for any resistive circuit what
do you see that current is always equal
to the voltage divided by the resistance
so here in this case in this circuit
where in where you don't have any
resistance but you have an inductor
there also you have current is equal to
voltage divided by something analogous
to resistance that means in an inductive
circuit this Omega L acts as resistance
right so the resistance of an inductive
circuit is known as inductive reactance
so it was told that we will call this
term as inductive reactance so what is
inductive reactance inductive reactance
is the resistance associated with a pure
inductive circuit wipe your inductive
circuit because if the circuit will have
any other circuit element except
inductor in that case the resistance of
that element will also come into picture
for example if you have a resistor as
well as an inductor in a circuit you
there will be two resistances involved
one is the normal resistance and of the
resistor and the other one is the
inductive rest
tens of them inductor right so we are
talking about inductive reactance which
is the resistance associated with a pure
inductive AC circuit that means the
resistance associated with an inductor
is your inductive resistance and we
denote it by X L X within subs with a
subscript L the subscript n represents
inductor the SI unit will be Oh SI unit
and dimensions everything remain the
same as that of resistance because this
ax this also acts as a resistance so its
function is also similar to resistance
it limits the current flowing through an
inductive circuit like how your
resistance limits the current flowing
through a resistive circuit right so in
this case we say that the inductive
reactance X L is equal to Omega L that
means the inductive reactance is
directly proportional to omega it is
directly proportional to L that means
greater the value of the inductance of
an inductive greater is the inductive
reactance similarly greated is the
frequency or the undulate frequency
greater is the inductive reactance so
this this was something new which was
introduced in case of an inductive
circuit right thank you please visit
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