I had this question on my exam and I got part a correctly, but part b incorrectly, and I honestly don't understand it. If someone could help explain it to me, you don't even need to solve it for me or anything... I would appreciate it.

Here it is:

Let's say you have a magnetic core with infinitely high permeability (like in an "ideal" transformer") and it has three legs (leg A, left, B, center, and C, right). The center leg has a coil wound around it with 200 turns and the resistance in that coil is 2.5 ohms. The magnetic core has a 5 x 5 cm uniform cross-sectional area. A DC voltage is applied to the coil. There are air gaps in the left and right legs of 2mm and 1mm, respectively.

a) Determine the voltage that will produce a flux density of 0.75 T in the right leg C, which contains the 1-mm air gap.
b) Find the magnetic flux in the other two legs of the core.

I honestly don't know what I'm doing with part b. I personally think the flux through the center has to be infinite (which is wrong) because the reluctance must be 0... where am I going wrong?

And the flux through the left leg A I think should be equal to the flux density multiplied by the cross sectional area... but which flux density? The one through the right leg, C? Why?

Thanks for your help,
-blazed

 

Calculate the MMF created by the current through the coil. Because the core has a relactance of 0, all the MMF will appear across the air gaps. Calculate the flux through each air gap and then add the two fluxes to take the flux through the center leg.

 

Calculate the MMF created by the current through the coil. Because the core has a relactance of 0, all the MMF will appear across the air gaps. Calculate the flux through each air gap and then add the two fluxes to take the flux through the center leg.

So if I'm understanding this correctly I calculate the flux in A using the V/R, the V I found in part a, as I, calculate the flux in C, and then the flux in B is the flux in A + flux in C?

Thanks again,
-blazed

 

flux=MMF/S and not V/R

S=reluctance

Yes, you calculate flux through A and then use the same MMF to find flux in C. Then flux in B=fluxA+fluxC.