Mutual inductance coefficient with so little info

[Granger]

Homework Statement

I have the following circuit:

The two inductors are connected in series are characterized by internal resistances R1 and R2 and self-inductances L11 and L22. The magnetic coupling factor between the inductors is k = 0.75. The inductors carry the same current i. What is the mutual inductance between inductors?

Homework Equations

3. The Attempt at a Solution [/B]
So I thought of applying:

$$K=\frac{|L_M|}{\sqrt{L_1 L_2}}$$

However:
(a) this does not tell me about the sign of $L_M$ (concordant or discordant coupling)
(b) I don't now the self-inductances BUT THEY ARE DIFFERENT.

What should I do with so little numerical info? Any tips?

 

[gneill]

(a) this does not tell me about the sign of $L_M$ (concordant or discordant coupling)
(b) I don't now the self-inductances BUT THEY ARE DIFFERENT.

What should I do with so little numerical info? Any tips?

I'd look at the diagram and note the winding directions.

 

[Granger]

I'd look at the diagram and note the winding directions.

For what I understand it is leftwards on the left windings and rightwards on the right windings, correct?

 

[gneill]

For what I understand it is leftwards on the left windings and rightwards on the right windings, correct?

I'm not sure how to interpret "leftward" and "rightward", but certainly they are wound with opposite sense.

Thus you should be able to place "dots" on the inductors appropriately.

 

[Granger]

I'm not sure how to interpret "leftward" and "rightward", but certainly they are wound with opposite sense.

Thus you should be able to place "dots" on the inductors appropriately.

I meant that B is directed to the right on the windings on the right and to the left on windings on the left! I'm sorry I'm not getting there, what does place the dots even mean?

 

[gneill]

I meant that B is directed to the right on the windings on the right and to the left on windings on the left! I'm sorry I'm not getting there, what does place the dots even mean?

Have you not been introduced to Dot Notation for coupled inductors? When looking at a schematic it allows one to interpret how coupled inductances are oriented with respect to each other (their winding senses). But it's not critical here since you can see this relationship directly in your figure.

 

[Granger]

Have you not been introduced to Dot Notation for coupled inductors? When looking at a schematic it allows one to interpret how coupled inductances are oriented with respect to each other (their winding senses). But it's not critical here since you can see this relationship directly in your figure.

No I haven't :/ That's why I'm missing something here. I came across the formulas for coupling inductors:

$ L= L1 + L2 + 2M $

$L = L1 + L2 - 2M $

And didn't understand where they came from and the meaning of them. Maybe it has something to do with that dot notation? Do you know where I can find info on that?

 

[gneill]

And didn't understand where they came from and the meaning of them. Maybe it has something to do with that dot notation? Do you know where I can find info on that?

Yes and yes.

A Google search on "mutual inductance dot notation" will turn up a bunch of tutorials including videos.

 

[Granger]

Yes and yes.

A Google search on "mutual inductance dot notation" will turn up a bunch of tutorials including videos.

Ok, so I looked on some tutorials on the internet and I'm more familiar with the concept now.

This leads me to obtain:

$$ \frac{\psi_1 \psi_2}{I}=L_1 + L_2 - 2 |L_M|$$

Where I take the absolute value to reinforce that we have discordant coupling (because of that the value of the mutual inductance will be negative and the minus sign will disappear).

Ok now what can I do next? Because I still don't know the self-inductances...

 

[gneill]

Ok now what can I do next? Because I still don't know the self-inductances...

You'd need to know something more about the circuit, such as voltage and current values.

 

[Granger]

You'd need to know something more about the circuit, such as voltage and current values.

I'm only told that I have a sinusoidal current but not a single value is provided... There must be another way :/

 

[gneill]

I'm only told that I have a sinusoidal current but not a single value is provided... There must be another way :/

Nope. You can only provide a symbolic result without more info.

 

[Granger]

Nope. You can only provide a symbolic result without more info.

Holy cow I just checked the document with the books mistakes and yup it should only be a symbolic result. Well at least all this time made me understand the dot notation which I wasn't really understanding so thanks :)

 

[gneill]

You're quite welcome.