Mutual Inductance Homework Help: Q4d Stuck, Need Advice

[billyray]

Homework Statement

I have included the questions and circuits. I have used previous post to help but am still stuck

Homework Equations

included in files

The Attempt at a Solution

I have worked hard to get to the question 4d. I am stuk because using previous posts to help I do not know if I need to use an admittance formula. I seem to get my answer from the resonance equation and the L equate one.

 

[gneill]

If you scroll down to the bottom of this page you'll see a section labelled:

Similar Discussions: Mutual inductance

Under it is a list of similar threads that might help you. In fact, the last one in the list is

Parallel Mutual Inductances

which handles the very same question.

 

[billyray]

o.k. i will go look at these. I have been looking though. i just don't understand why i need to solve admittance for. i just thought i put L equate into resonance equation and then use that in the big equation

with M=k*L

 

[billyray]

hi gneill
i am finding this equation in the post really hard:
So for the inductor and capacitor in parallel the total admittance is:

You're given values for C and ω, so it's a snap to find Leq if Y is zero.
I have gone through so many texts i have forgotten a lot. Do I need this equation or am i o.k with the resonance one that seems to give me L-equate that i need. Or am i wrong in thinking i can use a parallel inductor (L-equate) in the equation

my texts say nothing about using parallel inductors as L

 

[gneill]

I have gone through so many texts i have forgotten a lot. Do I need this equation or am i o.k with the resonance one that seems to give me L-equate that i need.

You can do either, as they both arrive at the same result. In fact, the formula that you call "the resonance one" can be derived from the other one, as resonance occurs when the admittance is minimized (equal to zero when it's just L and C involved).

 

[billyray]

Thanks gneill you have helped so much.
Is it ok to use L-equate in place of L in the equation?

 

[gneill]

Thanks gneill you have helped so much.
Is it ok to use L-equate in place of L in the equation?

That depends on what you mean by "L in the equation". If the equation is the one in post #3, then there is $L_T$, $L_1$, and $L_2$. Which one are you intending to replace by your L-equate?

 

[billyray]

i mean l -equate as l total

 

[billyray]

am I ok in solving as the upload above without the y equation

 

[gneill]

am I ok in solving as the upload above without the y equation

When you wrote:

You actually assumed that this would be the resonant frequency. That's okay if you are sure that it is so.

If you started with the admittance expression for the circuit (your "y equation"), setting y = 0 would lead to the same result, while also proving that your assumption was correct.

 

[billyray]

that is the equation in my book. I am sure its right you have me worried now?

 

[billyray]

im not sure my maths can do that though

 

[gneill]

that is the equation in my book. I am sure its right you have me worried now?

Don't worry. Either way you end up with the same expression for the resonant frequency for this circuit.

If the circuit had been more complicated, it's possible that the resonant frequency could be shifted away from $\omega = \frac{1}{\sqrt{L C}}$ by the introduction of damping terms. Then you'd want to start with the admittance or impedance expression in order to find the resonance. That method always works.

 

[billyray]

thanks gneill

i will come back to practicing the other equation when my maths gets better. Thanks for your help.