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inductive circuit question

Discussion in 'Electronic Basics' started by stephen hallacy, Oct 18, 2003.

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  1. Hello,

    I decided to review some electronics in my spare time. I came across
    an inductor circuit in my electric circuit's text book. The circuit
    is given below.

    -----------R1 (7.5k)-------------
    | |
    | |
    ----L1 (1.25H)--------L3 (6H)----
    | |
    ----L2 (10H)---
    |
    \\\

    The initial currents for L1, L2 and L3 are 2A, 2A and 0A respectively,
    and the currents are going from right to left in circuit shown above.
    I went through the math and came up with

    i1(t) = 2*exp(-1500*t)
    i2(t) = 5/4+3/4*exp(-1500*t)
    i3(t) = -5/4+5/4*exp(-1500*t)}

    where i1(t) is the current in L1, i2(t) is the current in L2 and i3(t)
    is the current in L3.

    I used the following differential equations to come up with the
    solution:

    d(i1(t))/dt - d(i2(t))/dt - d(i3(t))/dt = 0
    10*d(i2(t))/dt - 6*d(i3(t))/dt = 0
    10*d(i2(t))/dt + 1.25*d(i1(t))/dt + 7500*i1(t) = 0

    The currents should go to zero, however, the equations show that i2(t)
    and i3(t) approach 1.25 Amps. Am I doing something wrong?

    By the way, OrCAD Pspice showed the same result.

    Regards,
    Stephen
     
  2. Roy McCammon

    Roy McCammon Guest

    Put some small resistance in series with each inductor and try again.
    That loop composed entirely of two ideal inductors may be giving
    you strange results.
     
  3. John Larkin

    John Larkin Guest

    L2 and L3 can indeed circulate a current forever.

    John
     
  4. John Larkin

    John Larkin Guest


    Ever heard of NMR? MRI? They both use big superconductive magnets.
    They are shipped warm, and cooled down on-site with liquid nitrogen,
    then liquid helium. Once it's cold, a big power supply is connected to
    run the current up to a few kiloamps, then a shorting link is closed,
    and the power supply is loaded on a truck and taken away. The current
    circulates roughly forever, and the magnetic field is stable [1] as
    long as the helium level is kept up. Helium is topped off every few
    months to correct for boiloff.

    John

    [1] high-field superconductive magnets are subject to a bit of
    pinned-domain slipping, which causes the field to droop very slightly
    with time, generally in the 1 PPM per day sort of range. I think this
    eventually levels out as things settle.

    These things are hell on credit cards and hand tools.
     
  5. Baphomet

    Baphomet Guest

    Only if you believe in perpetual motion ;-) By the way, I have this
    bridge........
     
  6. Baphomet

    Baphomet Guest


    Point well taken John...but as long as energy from an outside source,
    however infrequently, must be supplied, it ain't perpetual...pretty darn
    close though ;-)

     

  7. Thanks for the response guys.

    I agree John. For this ideal component circuit, the current circulates forever.

    Stephen
     
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