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ALL ABOUT ELECTRONICS.
And today we will see Dot Convention in Magnetically
Coupled Circuit.
So, earlier we had seen the self-inductance
and mutual inductance in the electrical circuit.
And in the mutual inductance we had seen that,
whenever the current I flows through the coil,
it produces the voltage in the nearby coil.
So, whenever the current I flows through one
coil, the flux of one coil gets coupled to
the another coil.
And this kind of circuits is known as the
magnetically coupled circuit.
And the voltage that is induced in the nearby
coil can be given as V= M(di1/dt).
Where M is the mutual inductance between the
two coils.
Now here the polarity of the voltage that
is induced in the nearby coil depends upon
the way windings have been wound around the
core.
So, let's understand this.
So, here we have one core.
And on this core, two windings have been wound.
The one winding has been wound from the right
to the left.
While the second winding has been wound from
the left to the right.
Now, whenever we apply the voltage to this
coil number one, then the current I will flow
through this coil.
And using the right-hand thumb rule we can
find the direction of the flux that is flowing
through this coil 1.
So as the current is flowing in this direction,
the direction of flux will be in the downward
direction.
So, the flux will flow in the downward direction.
Let's say this is flux ɸ1.
Now, if we apply the voltage in the second
coil, then the current will flow in this direction.
So, using the right-hand thumb rule we can
find the direction of flux in the coil 2.
So, as current is flowing in this way the
direction of flux will be in the upward direction.
So the flux that is produced in the coil 2
will flow in the upward direction.
Now, if the current I1 and I2 are flowing
simultaneously then the flux which is produced
by this coil 1 and 2 will be flowing in this
direction.
So, as you can see here these two fluxes are
aiding to each other.
So, the voltage that is generated by the mutual
coupling between the two coils will be positive.
So, let's say V21 is the voltage that is developed
because of the current that is flowing in
the coil 1.
So this V21 can be given as V21= M(di1/dt).
And the polarity of this voltage will be positive.
Similarly, let's say V12 is the voltage that
is induced in the coil 1 because of the current
that is flowing in the coil 2.
And the value of this voltage can be given
as
V12= M(di2/dt)
And here, both the voltages will be positive.
Now, if we also include the self-induced emf,
then the expression for the voltage V1 will
be the,
V1= L1*(di1/dt) + M*(di2/dt)
Now, here the first term represents the self-induced
emf in the coil 1.
While the second term represents the induced
emf due to the coil 2.
Similarly, the voltage V2 can be represented
by
V2=L2*(di2/dt) + M*(di1/dt)
So, here also similarly the first term represents
the self-induced emf in the coil 2 while the
second term represents the voltage that is
induced due to mutual coupling.
Now, let's see what happens when we change
the direction of any of the one winding.
So, here we have kept the winding 1 as it
is but we have changed the direction of winding
in the coil 2.
So, now if we apply a voltage in coil 1, then
current will flow in this way.
And the flux which will be produced due to
this flow of current will be in the downward
direction.
Now, let's apply the voltage to the coil 2.
So, the current will flow in this direction.
Now, as we have changed the direction of winding,
the flux that has been generated will flow
in opposite direction and that can be found
using the right-hand thumb rule.
So, here as the current is flowing in this
direction, induced flux will flow in a downward
direction.
So, now if we apply this current I1 and I2
simultaneously, the flux which is produced
by these coils will flow in this direction.
So, as you can see here, the direction of
this flux ɸ1 and ɸ2 are opposite.
So, they will cut each other.
So, the induced voltage in the coils due to
the mutual coupling will be negative.
So, let's say V21 is the voltage that is induced
in the coil 2 due to the current that is flowing
in the coil 1.
And it can be given by equation
V21= -M*(di1/dt)
Similarly, let's say V12 is the voltage that
is induced in the coil 1 due to the current
that is flowing in this coil 2.
And it can be given by the equation,
V12= -M*(di2/dt)
Where M is the mutual inductance between this
two coils.
So, here as you can see, the polarity of the
induced voltage is negative.
So, now if we include the self-induced emf,
then we can write the expression for V1 as
V1= L1*(di1/dt) - M*(di2/dt)
Where the first term represents the self-induced
emf of the coil,
while the second term represents the induced
emf due to mutual coupling.
Similarly, the expression for V2 can be given
as
V2= L2*(di2/dt) - M*(di1/dt)
So, as you can see here the polarity of induced
voltage depends upon the way the windings
have been wound around the core.
So, every time if you want to find the polarity
of this voltage, first you need to check the
direction of this windings
And then you need to see the direction of
the flux.
So, this is a very lengthy process.
So to eliminate this process and make life
simple,
we use dot convention.
So, in the dot convention, we used to put
a dot on the either side of the coil and we
put this dot on the all the coils which are
coupled together.
Now, depending on the current, which is entering
or leaving the dot, we used to determine the
polarity of the induced voltage due to this
mutual coupling.
So, let's understand this dot convention.
So, if two currents are entering or leaving
the dot at the same time, then the voltage
that is generated due to mutual coupling will
be positive.
So, here let's take the first example which
we had already seen.
So, in the first example, we had seen that
the flux which is generated due to this coils
are aiding together.
So, the induced voltage due to the mutual
coupling is positive.
So, in that example, if we simply put the
dot on these two sides of the coil, then by
using the dot convention we can easily find
the polarity of the induced voltage.
So, as you can see here, the current I1and
I2 are entering the dots.
So, the induced voltage due to the mutual
inductance will be positive.
Or in the same example if we put a dot on
the other side of the coil, then also you
can see here, the current is leaving the dots
at the same time.
So, the induced voltage in the both the coils
is positive.
Also, one more thing about the dot is that,
whatever polarity of the voltage that appears
across the dotted terminal, the same polarity
of the voltage will appear at the other side
of the dotted terminal.
So, here as you can see, at the dotted terminal
the polarity of the voltage is negative, so
on the other side also at the dotted terminal,
the polarity of the voltage will remain negative.
So, even if you don't know the value of this
current I1 and I2 or the direction of this
current I1 and I2, then also you can find
the polarity of the induced voltage.
Now, let's see what happens when one current
is entering the dot and another current is
leaving the dot.
So, if one current is entering the dot and
another current is leaving the dot, then the
generated voltage due to the mutual coupling
will be negative.
So, here we have taken the second example.
So, in the second example, we have seen that
the flux ɸ1 and ɸ2 are cutting each other.
So, the value of induced voltage due to mutual
coupling is negative.
So in this winding, suppose we had given dot
at these two points, then just by applying
dot convention we can easily find the polarity
of the induced voltage.
So, as you can see here,
one current is leaving the dot while another
current is entering the dot.
So, the voltage that is generated due to the
mutual coupling will be negative.
So, in this way using the dot convention we
can easily find the polarity of the induced
voltage.
So, schematically we can represent this winding
by a simple symbol of an inductor.
So, we can represent this winding by this
symbol.
And here line between the two coils represents
that the winding has been wound on the same
core.
So, in this way using the dot convention,
the direction of winding as well as the polarity
of the induced voltage has been taken care
of.
So, now suppose if we have given this schematic,
then using the dot convention we can easily
find the polarity of the induced voltage.
As as you can see here, the current I1 and
I2 are entering the dots.
So, the voltage that is induced due to the
mutual coupling will be positive.
So, let's say voltage V1 is the voltage across
the coil 1.
And voltage V2 is the voltage across the coil
2.
So, we can write the expression for V1 as
V1= L1*(di1/dt) + M*(di2/dt)
Where L1 is the self-inductance of this coil.
And M is the mutual inductance between this
two coils.
Similarly, the expression for V2 will be
V2= L2*(di2/dt) + M*(di1/dt)
Where L2 is the self-inductance of this coil
and M is the mutual inductance between these
two coils.
Now, the same expression is valid for the
second schematic.
As, in the second schematic if you see, the
current I1 and I2 are leaving the dot at the
same time.
Now, if you see the third schematic, the current
I1 is leaving the dot, while current I2 is
entering the dot.
so, the voltage that is induced due to the
mutual coupling will be negative.
So, let's say here voltage across this coil
is V1 and the voltage across the second coil
is V2.
So, here the expression for V1 will be
V1= L1*(di1/dt) - M*(di2/dt)
Similarly, the expression for V2 will be
V2= L2*(di2/dt) - M*(di1/dt)
Where M is the mutual inductance between the
coil 1 and 2.
Now the same expression is valid for the second
schematic.
So, here in this schematic if you see, the
current I1 is entering the dot while current
I2 is leaving the dot.
So, the value of voltage due to the mutual
coupling will be negative.
So, now let's see the expression for the coils
which are mutually coupled and connected in
series.
So, here as you can see the two coils are
connected in series.
The L1 and L2 are the inductance of this two
coils.
And the mutual inductance between the two
coil is M.
So, if you see here The current I is entering
the dot in the first coil.
The same current I is flowing this coil 2.
And it is entering the dot in the coil 2.
So, the flux that is generated due to this
coil 1 and 2 will be additive.
So, this type of series connection is known
as series aiding connection.
And the value of the equivalent inductance
will be
Leq= L1 + L2 + 2M
Similarly, if we put the dot from one end
to the another end of the coil, then also
the same expression is valid.
As you can see here, the current I is leaving
the dot in both coils.
So, this is also series aiding connection.
And the value of the equivalent inductance
will be
Leq= L1 + L2 + 2M
Now, let's see the expression for the equivalent
inductance when one dot is at one end of the
coil and another dot is at another end of
the coil.
So, if you see here, the current I is entering
the dot in one coil, while it is leaving the
dot in another coil.
So, this kind of series connection is known
as series opposing connection.
As the flux in the both the coils is cutting
each other.
So, the value of equivalent inductance can
be given as
Leq= L1 + L2 -2M
Similarly, this configuration is a series
opposing connection.
Because here also the current I is leaving
the dot in one coil, while it is entering
the dot in another coil.
So, this is also series opposing connection.
And the value of equivalent inductance will
be
Leq= L1 + L2 -2M
So, now let's see mutually coupled coils which
are connected in parallel.
So, here we have two coils which are connected
in parallel.
let's say that current I is entering this
coil.
Out of this current I, current I1 is flowing
through this coil 1 and current I2 is flowing
through this coil 2.
So, here as you can see, the current I1 and
I2 are entering the dots.
So, this is an example of parallel aiding
connection.
And their equivalent inductance can be given
as
Leq= (L1L2- M^2)/(L1+L2-2M)
And the same expression is valid when dots
are put at the bottom of the two coils.
So, let's say the current I is flowing in
this circuit.
The current I1 is flowing through this coil
1 and current I2 is flowing through this coil
2.
So, here also the current is leaving the dot
at the same time.
So, this also is an example of parallel aiding
connection.
And the value of the equivalent inductance
can be given by this expression.
So, now let's see the value of equivalent
inductance when two coils are connected in
parallel opposing connection.
So, here let's say current I is entering into
this circuit.
Out of this current I, the current I1 is flowing
through this coil 1 and current I2 is flowing
through this coil 2.
So as you can see here, the current I1 is
entering the dot while current I2 is leaving
the dot.
So this is the example of the parallel opposing
connection.
As the flux in the both the coils is cutting
each other.
The value of equivalent inductance can be given
by this expression.
That is
Leq= (L1*L2 - M^2)/(L1 + L2 + 2M)
So, if you want me to derive the expression
for series and parallel combination, then
please let me know in the comment section
below.
So far we had seen that only two coils are
coupled together.
Now, let's see if more than two coils are
coupled to each other.
So, here as you can see we have three coils,
one, two and three which are mutually coupled
to each other.
Now, to represent the mutual coupling between
each other, we need to use different dot symbols.
So, let's say this two dots represents the
mutual coupling between the one and two.
While the square dots represents the mutual
coupling between the coil 1 and 3.
And the triangular dots represents the mutual
coupling between the coil 2 and 3.
So in this way, if more than two coils which
are mutually coupled to each other are connected
together, then using this different dot symbols
we can represent the mutual coupling between
them.
So, I hope you understood what is dot convention
in the magnetically coupled circuit.
We will see more examples based on the dot
convention in the upcoming videos.
