Finding inductance of a circuit

[dhruv.tara]

NOTE: This is not a homework problem, so do not shift it.

The question is as follows, I am given a core having an air gap wounded by a coil, I am given area of core, gap. Length of core and gap. number of turns. Permeability of core and air gap and magnetic field in the core (I assume no leakage flux too) And I am required to find the inductance of the coil used.

I had a formula L = N^2*MuCore*MuO*AreaCore/lengthCore
I used it and got wrong answer. I realized that probably this formula was derived assuming no air gaps and that is why I got the answer wrongly.

I changed to the formula L=N*Flux/Current and got the answer correctly (in fact book I am following also uses the same approach)

But I realize that the formula L = N*Flux/Current was derived using the value of inductance written above (assuming that there is no air gap) So how does this time the new formula works?

According to me
L = N^2*MuCore*MuO*AreaCore*AreaGap/(LenCore*AGap + LGap*ACore)

(answer seems to be wrong using above formula too)

Any help is appreciated.

 

[SirAskalot]

Why not try to calculate the reluctance of the core and air-gap by them self, add them togther and then divide N^2 by the total reluctance. L=N^2/R or L= N^2*P where P(permanence)=1/R(reluctance)

Also fringing in the air gap should be taken into account.

If you get the right answer, then you can begin to combine the equations, altough i don't see why there is a reason for that, your understanding of the subject is going to be poor if you are just to remember the specific equation, and not see the relations between reluctance, inductance, permanence, flux and magnetomotive force.

There is also a possibility that the answer in the book is wrong.

 

[dhruv.tara]

Why not try to calculate the reluctance of the core and air-gap by them self, add them togther and then divide N^2 by the total reluctance. L=N^2/R or L= N^2*P where P(permanence)=1/R(reluctance)

Also fringing in the air gap should be taken into account.

If you get the right answer, then you can begin to combine the equations, altough i don't see why there is a reason for that, your understanding of the subject is going to be poor if you are just to remember the specific equation, and not see the relations between reluctance, inductance, permanence, flux and magnetomotive force.

There is also a possibility that the answer in the book is wrong.

Thank you for your reply, please help me a little further.

No I get the way you are mentioning. In fact my book also solves the problem in quite a similar fashion. What I don't get is that how we are able to use this equation because my current understanding of calculating inductances in such problems is as following:

phi (magnetic flux) = mmf/R(reluctance,total)
phi = NI*mu*area/length

then we use Faraday's law e=-nd(phi)/dt
so we get e = (n^2*mu*area/length)*d(I)/dt
now quantitatively we say that the coefficient of d(I)/dt in the above equation is the value of inductance.

Using this definition of inductance we derive L=N*phi/I (the form that you are probably using, and my book precisely uses)
Here we take phi as NI/RelucatanceTotal
phi = NI/(Rcore + Rgap)
we calculate individual reluctances and put in L=N*phi/I and get correct L.

But my problem with that solution is that the equation we are using L=N*phi/I is itself derived by considering that we have no air gaps or any such non-uniformity in the core.
(Because in deriving this formula we used L=N^2*mu*Area/Length which was derived for a uniform core)

Any help is appreciated.