Calculate Equivalent Inductance of Coils Connected in Series

[regisz90]

Homework Statement

There are two coils wined around the same closed iron core. Their inductances on this iron core are measured to be 4 henry, and 9 henry. Then the two coils are connected in series. What will the equivalent inductance be?

Homework Equations

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The Attempt at a Solution

I think that the measured values aren´t the inductances of the coils, but there is also some mutual inductance. The equivalent inductance in series will be L=L₁+L₂+2M
I just don't know that the 4 Henry and the 9 Henry are in what relation with the L₁ and L₂ inductances(without mutual)

 

[berkeman]

Homework Statement

There are two coils wined around the same closed iron core. Their inductances on this iron core are measured to be 4 henry, and 9 henry. Then the two coils are connected in series. What will the equivalent inductance be?

Homework Equations

...

The Attempt at a Solution

I think that the measured values aren´t the inductances of the coils, but there is also some mutual inductance. The equivalent inductance in series will be L=L₁+L₂+2M
I just don't know that the 4 Henry and the 9 Henry are in what relation with the L₁ and L₂ inductances(without mutual)

Hint -- the inductance is proportional to the number of turns __________ (fill in the blank).

 

[regisz90]

squared?

 

[berkeman]

squared?

Yep!

So if you combine two equal coils L1 and L2, you don't get L1+L2, you get ________

And now how can you use this to solve this problem?

 

[regisz90]

its proportional squared, so if the number of turns are N1 and N2, then we get L=k*(N1+N2)^2=k*N1^2 + k*N2^2 + 2*k*N1*N2=L1 + L2 + 2*sqrt(L1*L2).
But I don't know how can i use this to solve the problem. The result is the inductance of the two coils together, and they tried to measure them separately on the same iron core, but i don't know what their result is. L1 and L2? or L1+sqrt(L1*L2) and L2+sqrt(L1*L2)?

 

[berkeman]

its proportional squared, so if the number of turns are N1 and N2, then we get L=k*(N1+N2)^2=k*N1^2 + k*N2^2 + 2*k*N1*N2=L1 + L2 + 2*sqrt(L1*L2).
But I don't know how can i use this to solve the problem. The result is the inductance of the two coils together, and they tried to measure them separately on the same iron core, but i don't know what their result is. L1 and L2? or L1+sqrt(L1*L2) and L2+sqrt(L1*L2)?

Try making up some numbers for the inductance versus the number of turns squared. The two coils are on the same core, so they will have the same inductance per number of turns squared. Work out the total inductance from there...