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Mutual inductance / equivalent inductor

  1. Oct 31, 2016 #1
    1. The problem statement, all variables and given/known data
    q4_tma_diagram.jpg

    2. Relevant equations
    See if you can show that L##_1## and L##_2## as in (a) can be replaced by the equivalent inductor L##_{eq}## as in (b):

    $$L_{eq} = \frac {L_1 L_2 - M^2 } {L_1 + L_2 - 2M }
    $$
    3. The attempt at a solution
    Um, I don't really know where to start because I don't really understand what the question is asking. Am I supposed to provide some 'proof' in algebraic form? Thus I don't know the form that the answer should take, as in what equals what.

    A gentle nudge would get me moving :)
     
  2. jcsd
  3. Oct 31, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Just like reducing a resistor network to a single equivalent resistance, they want you to reduce the inductor network to a single equivalent inductor. The tricky bit is handling the mutual inductance. How you go about it is up to you, but consider driving the circuit with ac test voltage V and finding the resulting current it supplies. Then compare to the expression for the current if the load was just a single inductor Leq.
     
  4. Oct 31, 2016 #3
    Thank you. I shall post my attempt for scrutiny!
     
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