The next parameter that
we study is inductance.
Basically, what is inductance,
inductance is a property by
which an element opposes the
change in current, resistance
opposes the flow of current and
inductance opposes change in
current, that is If ever a
constant current is flowing
through element that is current
is not changing, then inductance
does not come into picture okay.
So, in case of constant current
inductance has no role.
inductance usually we are
considering here as a self
inductance, self inductance
means, we apply a voltage or a
current to the coil and emf is
induced in the same coil that is
known as self inductance, that
is a coil is responsible for
inducing the EMF within itself
it is known as self inductance.
That is why it is being
represented by L. Now, with the
inductor we associate a concept
of flux linkage,that is the
amount of flux linking a coil.
Let us denote the flux linkage
by phi, which is equal to L into
I flux link is equals to L
intoI. I is the current flowing
through the inductor. By
faraday's law, EMF induce is
equal to d phi by dt. Now put
the value of phi and
differentiate it it will become
Ldi by dt. L is time invariant
So, it will come outside okay
that is voltage across inductor
is given by Ldi by dt and it is
represented like this in terms
of coil
This is the current flowing into
the inductor
This is the voltage across the
inductor and it has inductance L
Okay. Now, if you want to go
into the Laplace domain to go
into the Laplace domain we take
a laplace on both both sides it
becomes V(s)  is equals to L
into s into I(s) okay L times s
into I(s), basically Laplace of
derivatives s into I(s), from
here we get V(s) upon I(s) is
equals to s into L. Here we have
assumed zero initial condition,
that is V(s) upon I(s) equals to
S into L. So, in Laplace domain
inductor is model as s times L,
Is it fine
and how do we determine the
current in the inductor
current in the inductor is given
by one by L integral of v into
dt. Here also if you take
Laplace it becomes I(s) is
equals to one by L into V(s)
upon s, okay Laplace of integral
is V(s) upon s. So, we are
getting the same relation. So,
that is how we model a inductor.
Now, let us understand the power
and energy of a  inductor, as I
told you power in electrical
circuit is given by voltage into
current. Now put the value of
voltage that is Ldi  by dt
voltage is equal to L di by dt
into current. Now again it
becomes Li di by dt. So, power
is equals to Li di by dt. Now if
you Want to determine the energy
it is integral of Pdt, now this
power is known as instantaneous
power because
we are taking a current as a
function
of time. So, this power also
vary with time. Now put the
value of power here, P is equals
to Li di by dt into dt okay. So
it becomes take L outside and dt
dt get cancelled, we get idi no
integration of idi is equal to
half i square, so it becomes
half Li square okay. So, this is
the energy of inductor or you
can say it is the energy is
stored in an inductor that is
half Li square. Now, if we take
a DC current that is current is
constant.
Now, what is the voltage across
the inductor we know
that voltage is L di by dt. So,
di by dt is zero here, because
current is constant, so voltage
becomes zero. Therefore power
will also be zero because power
is v times I Power is also zero,
but the energy is constant that
is half Li square that is
inductor does not store any more
energy if you're giving a DC
excitation Okay. Now usually
inductance follow Faraday's law
or you can even say it follows
Lenz law, what is Lenz law that
effect opposes the cause. Now,
here you can see due to change
of current due to di by dt
voltage is being induced in the
inductor this voltage will
oppose this change in current
that is why I told you earlier
inductance always opposes the
change of current okay. It is
actually known as magnetic
inertia. Just know I told you
inductance associated with the
flux linkage, whenever flux is
linking with any type of
element, then that flux cannot
change instantaneously that is
magnetic inertia. If flux cannot
change instantaneously, so is
the current. So, inductor
current can never change
instantaneously , it is also
known as current stiff element.
suddenly the current cannot
change Is it fine. So, that is a
basic property of inductor it
will be used when we will study
transient analysis. when we talk
about practical inductor,
inductor is nothing but a coil,
a coil will be formed by means
of conducting material and
conducting material has a
property which we studied just
now that it has a resistance.
So, practical inductors
aremodeled like this a
resistance in series with a
inductor Okay. That means, when
we talk about practical
inductors some part of energy
will be converted into heat and
some will be stored in the
inductor. How does the inductor
store energy ,it store this
amount of energy half Li square
in its electromagnetic form,
that is it will store energy in
the form of current flowing
through the inductor coil and it
will store that and it will
tored that energy in magnetic 
omain. There are various domain
for energy like electrical
domain in which we talk about
resistance energy magnetic domai
 in terms of inductor mechanica
domain if we talk about torqu
 or we can talk about inertia
Now, what is the practica
 application of inductors, th
y are used in filters, compensa
or, current limiting reacto
in  communication as well as i
 power system. Currently limi
ing reactor means whenever ther
 will be a fault this indu
tor will limit the amount of c
rrent flowing through the faul
okay. And filter they will be u
ed in LC filter and they will
be filtering out noise when you 
re talking or when there is a co
munication channel then nois
 must be filtered out so that
a signal can be easily tran
mitted okay.
