Why Is Calculating Reluctance with an Air Gap Confusing?

[JoeMarsh2017]

Homework Statement

Homework Equations

Reluctance = small "L"/mu*A

The Attempt at a Solution

I went the route of using B/H=Mu ...since we know that B=1.2Tesla's and Mu=4pi*10^-7 we arrive at our "magnetic field intensity "H" as 954,929.7 H"

BUT if I am trying to find Reluctance... then we have to consider the air gap...Im getting lost because the mean length would small "L" + air gap? Right?

This should be so simple but I am missing something...
Utilizing the magnetization curve is also confusing for me..see picture

Thanks for your help in advance, I am stuck, willing to ask for help, and I want to learn!

JOE[/B]

 

[JoeMarsh2017]

We also have

 

[cnh1995]

We also have View attachment 111613

Hi Joe.. Welcome to PF!

You can get the value of relative permeability of the core for B=1.2T from the magnetization graph.
Once you have the relative permeability of the core, all you need to do is simplify the magnetic circuit.

 

[JoeMarsh2017]

I think then, if I go across from 1.2T, the Relative Perm = 6000 ?

 

[cnh1995]

I think then, if I go across from 1.2T, the Relative Perm = 6000 ?

Yes.

 

[JoeMarsh2017]

Ok..So that means MUr=Mu/Mu(zero) = 6000/4pi*10^-7 =4.712x10^-4 which = Mu
*A
I can now go into my Reluctance formula Fancy "R" =small "L" / Mu*A to figure my Reluctance for the core

then-
Lcore - 52cm which converts to 0.0052 m/4.712x10^-4 x 0.0018 = 0.001986 Reluctance of Lcore
Lgap -14cm which converts to 0.0014 m/4.712x10^-4 x .0018 = 0.005348 Reluctance of Lgap

Add them together for Total series Reluctance = 0.001986+0.005348 = 0.007334 Total Reluctance

 

[JoeMarsh2017]

flux x reluctance= number of turns x current

flux x reluctance/number of turns =current

Then I know the current

 

[JoeMarsh2017]

once I know the current, I can multiply against the 64 ohms resistance to tell me the voltage across the gap?
In my head this seems way too easy!
JOE

 

[JoeMarsh2017]

OK=nexy questions, now my brain wheels are turning...

Since this magnetic circuit is a series circuit, is the gap creating a Positive top part of the core, and a negative bottom part of the core! This would explain why the voltage drop is across the gap.. Am I right?

JOE

 

[cnh1995]

once I know the current, I can multiply against the 64 ohms resistance to tell me the voltage across the gap? **voltage of the battery** There's no voltage across the gap.
In my head this seems way too easy!
JOE

Right.

OK=nexy questions, now my brain wheels are turning...

Since this magnetic circuit is a series circuit, is the gap creating a Positive top part of the core, and a negative bottom part of the core! This would explain why the voltage **mmf** drop is across the gap.. Am I right?

JOE

Right. You can see that the mmf drop Φxs is very high across the air gap.

 

[JoeMarsh2017]

I see.. Yes Voltage is the Battery "E" which is applied across the winding's at 64 Ohms..

The question for the problem=

Since I know the current now, and I have the resistance, I now know the voltage at the battery

 

[cnh1995]

I see.. Yes Voltage is the Battery "E" which is applied across the winding's at 64 Ohms..

The question for the problem=View attachment 111615
Since I know the current now, and I have the resistance, I now know the voltage at the battery

Right.
I didn't check your earlier calculations but your steps are all correct. Check the reluctance values again. I think air gap reluctance should be very high.

 

[JoeMarsh2017]

 

[cnh1995]

View attachment 111616

That doesn't look right. Voltage and current are too small.

Ok..So that means MUr=Mu/Mu(zero) = 6000/4pi*10^-7 =4.712x10^-4 which = Mu
*A

No. You should use the absolute permittivity μ, which is μ₀μ_r.
This was making your reluctances very small.

 

[rude man]

We also have View attachment 111613

First thing is to realize that the permeabilty of space is << any permeability in your iron or whatever your core comprises. So compute the reluctance of the air gap, then flux x reluctance = mmf = Hi.

If they want you to include the effects of finite core reluctance, shame on them!