Question on mutual inductance

Discussion in 'Homework Help' started by mentaaal, Dec 30, 2007.

  1. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Hey guys i was reviewing past papers in anticipation for my exam next saturday and i am stumped on a question, even reading the solution is confusing me as i dont think that we have ever really covered mutual inductance:

    (b)
    Consider two coils wound around plastic coil former, of 100 turns and 200 turns respectively. The two coils are magnetically-coupled, because 80% of the flux produced by one coil links the other coil. If the first coil is suddenly connected to a DC supply and its current rises linearly at a rate of 100 A/s and the self-induced e.m.f is 5 volts, then:
    (i) What is L, the self-inductance of the first coil?
    (ii) Find the mutually-induced e.m.f in the second coil.
    (iii) Determine the mutual inductance between the two coils.
    (iv) Determine the self inductance of the second coil.
    [8 marks]
    The only parts that i need help with are parts III and IV.
    I can get part III but am not entirely sure what it is or how to describe it. Is M: mutual inductance a measure of the second coils ability ... to induce a voltage to the first coil? How is the inducance of the second inductor found then?

    I know the formula for the inductance depending on the number of terms, the conductivity of the material its wrapped around, the area and the axial length. But i dont know how to apply the mutual conductance to solve this problem, nor do i fully understand it either, I have already looked this up in google and cant seem to find anything which helps me out.

    Cheers Guys!


     
  2. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    From my old textbook Network Analysis and Synthesis by Kuo:

    v1(t)=L1*di1/dt +M*di2/dt
    v2(t)=M*di1/dt+L2*di2/dt

    M=K*sqrt(L1*L2)

    Where K is the coupling coefficient (0.8 in your problem).

    Hope this helps.
     
  3. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Hi ron, it does indeed helps thanks, quick question though, is this the only way to find the self inductance of the second coil?
     
  4. Ron H

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    Is it safe to assume that the second coil's inductance is L1*(200turns/100turns)^2?
     
  5. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Well the answer to this question which i have is that L1 = 50mH and L2 = 100mh so.......?
     
  6. Ron H

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    Can you rationalize that answer with the rest of the information you have? The problem says they are wound on the same form, and inductance is proportional to the square of the number of turns, so how did they come up with L2=100mH?
    The second coil is apparently unloaded (open circuit), so there is no di2/dt. Given this fact, I don't see how you can calculate L2 except by the turns ratio. I think the answer you have is wrong.
     
  7. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    No problem at all, i am altogether confused by this so heres the teacher's answer:
     
  8. Ron H

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    I'm not sure where the (0.1)^2 came from, but it does not equal 0.02:

    EDIT: OK, now I see where the (0.1)^2 came from.
     
  9. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    So the correct answer is actually 200mh? Excellent thanks alot Ron!
     
  10. Ron H

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    Apr 14, 2005
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    That's how it looks to me. Let us know how this turns out!
     
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