#### Self Inductance and Mutual Inductance Explained

Hey, friends, welcome to the YouTube channel

ALL ABOUT ELECTRONICS, and today we will see what is Self Inductance and Mutual Inductance

in the electrical circuit. So, first, we will understand the concept

of self-inductance and mutual inductance and then we will derive the expression for the

self and the mutual inductance. So, let’s first see the inductance.

So, it is a property of the electric conductor by which the rate of change of current produces

the electromotive force or emf. So, let’s say we have one coil.

And the current I is flowing through this coil.

So, the rate of change of current through this coil produces emf or voltage.

Now, if this electromotive force or voltage is produced within that same coil then that

is called self-inductance. And if the rate of change of current produces

the emf or voltage in nearby coil then that is called mutual inductance.

So, let’s understand first the self-inductance. So as we have said earlier, the voltage or

emf that is generated is proportional to the rate of change of current.

So, we can write, V=- L* (di/dt) Where L is the self-inductance or simply inductance.

And the unit of the self-inductance or inductance is Henry.

So, you will observe negative sign. And this negative sign is because of the Lenz’s

law. So, according to the Lenz’s law, the generated

emf or voltage opposes the rate of change of current through which it is been generated.

So, here this negative sign implies the voltage that generated is opposes the rate of change

of current. So, let’s say this is equation number 1.

So, now let’s find the expression for this inductance in terms of magnetic flux.

So, let’s say we have one coil. And in this coil the current I is flowing.

So, because of flow of current, there will be a generation of magnetic flux phi.

And if the current that is flowing through this coil is varying with time,

or we can say that the current flowing through this coil is time varying then the magnetic

flux that will be generated will also be time varying.

So, this time varying magnetic flux produces the emf or voltage in this coil.

So, according to the Faraday’s law, the voltage that is induced in this coil can be given

as, V=-N*(dɸ/dt)

Where N is the number of turns in this coil. So, let’s say this equation number 2.

So, here we got two equations, so now let’s compare this two equations.

So, we can write, -L*(di/dt)=-N* (dɸ/dt)

Or we can write, L*di=N*dɸ

That means L*i=N* ɸ

Now here this N*ɸ also known as the flux linkage or magnetic flux linkage.

And sometimes it is also denoted by symbol ci.

So, we can write, L=N* (phi)/i

or (Ci)/i

So, this is the expression for inductance in terms of magnetic flux and the current.

So, now let’s see the mutual inductance. So, let’s here we have two coils one and two.

And the number of turns in this coils are N1 and N2 respectively.

Now let’s say the current i1 is flowing through this coil number 1.

And because of the flow of current, there is a generation of magnetic flux.

Let’s say that is ɸ1. So, now this magnetic flux will link with

this coil number 1 and 2. So, let’s say the ɸ11 is the flux that

is linked with the coil number 1. And ɸ12 is the flux that is linked with

this coil number 2. So, here the current that is flowing through

this coil number 1 is time varying. That is, it is varying with time.

So, because of that, the flux that is linked with this coil number 2 will also be a time-varying.

So, this time varying magnetic field will generate a voltage in this coil number 2.

And let’s say that is V2. So according to the Faraday’s law, we can

write, V2=- N2* (dɸ12)/dt)

Where N2 is a number of turns in this coil number 2.

Let’s say this is the equation number 3. Now, the voltage that is generated in this

coil number 2 is proportional to the rate of change of current in the coil number 1.

so, we can write V2 is proportional to the rate of change of current in the coil number

1. That means,

V2=-M*(di1/dt) Where M is nothing but mutual inductance between

this two coils. And here the negative sign implies the voltage

that is generated in the coil number 2 opposes the rate of change of current.

The unit of this mutual inductance is same as the self-inductance.

That is Henry. So, let’s say this is the equation number

4. So, now here we have got two equations 3 and

4. So, now let’s find the value of this mutual

inductance in terms of the magnetic flux. So, we can write

-M* (di1/dt)=-N2* (dɸ12/dt) or we can write,

M*(di1)=N2* d(ɸ12) That means,

M*i1=N2*ɸ12 So we can write,

M=N2*ɸ12/i1 So this is the expression for mutual inductance

when the current is flowing in the coil number 1.

Similarly, if the current is flowing in the coil number 2,

and because of that if the voltage is generated in the coil number 1 then the mutual inductance

M can be given as M=N1*ɸ21/i2

Where ɸ21 is the flux that is linked to the coil number 1 because of the current that

is flowing in the coil number 2. So, now we can write mutual inductance

M=(N2*ɸ12/i1)=(N1*ɸ21/i2) So, now here the coupling between the two

coil defines the how well the flux that is linked to the another coil.

If the coupling between the two coil is very good, then the flux that is linked to the

another coil will be the good. Similarly, if the coupling between the two

coil is bad then the flux that is linked to the another coil will be poor.

So, to define this coupling between the two coils,

we use a term Coefficient of coupling. That is the fraction of total flux that is

linked to the another coil. And it is denoted by symbol K.

So, let’s say ɸ1 is the total flux that is generated because of the current that is flowing

in the coil number 1. And out of this ɸ1, ɸ12 is the flux that

is linked to the coil number 2. And the ratio of flux (ɸ12/ɸ1) is known

as the coefficient of coupling. Similarly, if ɸ2 is the total flux, that

is generated because of the current flowing in the coil number 2,

And out of the total flux if the flux ɸ21 that is linked to the coil number 1, then

the ratio of this ɸ21/ɸ2 is known as the coefficient of coupling.

So, the value of this k is between the 0 and 1.

If the value of k is 1, that means the coupling between the two coil is 100%.

If the value of k is 0, then there is no coupling between the two coils.

So, now let’s just find the relation between the coefficient of coupling and the mutual

inductance. So, earlier we have found this expression

for mutual inductance. So, now let’s just multiply this two equations.

So, we can write, M^2=(N1*ɸ21/i2)*(N2*ɸ12/i1)

So, let’s just multiply and divide this term by ɸ1*ɸ2.

And by rearranging the terms we can write, (N1*ɸ1/i1)*(N2*ɸ2/i2)*(ɸ21/ɸ2)*(ɸ12/ɸ1)

So, as we have seen earlier, the first two So, as we have seen earlier, the first two terms are nothing but the self-inductance

of the coil 1 and 2. That is L1 and L2.

And if we observe the last two terms, they are nothing but the coefficient of coupling.

That is k. So, we can write them as k*k.

That means, M^2=K^2*L1*L2

That means, M=k*sqrt(L1*L2)

So, this is the expression between the mutual inductance and the coefficient of coupling.

So, now let’s just take one simple example and find the value of this coefficient of

coupling k. So, here we have given the values of L1, L2,

and M. And we need to find the value of this coefficient

of coupling. So, we can write K=M/(sqrt(L1*L2))

That is nothing but, 0.05/(sqrt(0.1*0.1))

That is equal to 0.05/0.1 So, the

value of coefficient of coupling k=0.5 So, in this way, if we have given the value

of self-inductance and mutual inductance then we can find the value of the coefficient of

coupling. Or in another way, we have given the value

of self-inductance and the coefficient of coupling, then we can find the value of this

mutual inductance. So, I hope you understood what is self-inductance

and the mutual inductance in the electrical circuit

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Where is dr/dt lol..

thank u sir for vailable speach

sir how is current induced in the same coil when we are changing i

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Wat i try to say here is dat… As a bro, try to explain as simple as possible first dan go to the derivation part…. By focus mre on layman explation than go toward complex part… Always.

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well said bro thank u soo much

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how do we visualise rate of change of current. Can u please explain soon as possible

सरल और सुन्दर

sir could you pls explain the difference between emf and voltage in some text books i found it is force and in some other it is not force so wheather it is force or not

Average not so god

So much helpful .. thank you

watched it at speed 1.25, perfect pace!

please upload working of transistor

Good explanation bro

Thanks a lot

Sir coefficient of coupling why we will calculate

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Great yar now o totaly understand

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great explanation , it should be a relation between the coeftion of coupling and the distance between the tow coils

Thanks it is easy to understand

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Thanks

Very helpful. Good job!

Question: If we move a magnet in front a coil and the magnetic flux φ, due to the magnetic field of the magnet, crossing this coil varies then an emf e1 = -dφ/dt is induced in the coil. If the induced current in the coil is also varies, is there a self induced emf in the coil such as e2 = -L di/dt ? and that you.

Thank you sir

Thank you

average.not so good

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Thank you! This was very helpful in understanding the content!

Super

Sir please reply me according to lenz law which quantity opposes the which quantity ? In detail

Best one i found on this topic yet!

Do you have a video on how to get the total inductance of a circuit? (With and without mutual inductance)

Thanks sir

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