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Homework Help: Differential equation to represent circuit

  1. Nov 27, 2011 #1
    **edit** This problem has been solved.

    For the circuit shown in the figure, find a differential equation the relates the input current i1(t) to the output voltage e0(t). Note that you cannot take a KVL across a current source because you cannot figure out the voltage drop across it.

    the circuit:


    my work so far:


    Am I on the right track? We never had any problems with a current source during the lectures, and I don't know if I can set the voltages of parallel branches equal like that.

    Any ideas will be greatly appreciated!! It has been very tough getting in touch with my professor over Thanksgiving break and this assignment is due tomorrow.
    Last edited: Nov 27, 2011
  2. jcsd
  3. Nov 27, 2011 #2


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    Staff: Mentor

    Hi TigerBrah, welcome to Physics Forums.

    You're doing pretty well with the problem, but I think you'll want to keep R2 in the equations (rather than substituting eo), since R2 influences the current in its branch. If you solve for the differential equation for the branch current, multiplying it through by R2 will give you the equation for the output voltage.

    Another approach would be to use mesh currents. The first loop's mesh current is set by the input current, so you only have one loop to deal with.

    Yet another approach would be to convert ii(t) and R1 into a Thevenin equivalent voltage source and series resistance. Then you'd have a simple voltage divider to solve!
  4. Nov 27, 2011 #3
    Thanks gneill!

    Using Mesh Currents is definitely the fastest way. I reworked the problem and got almost the same answer as above, but I also caught a mistake. My last term should be divided by R1.

    I was also able to check my work using a secondary method we learned in class using Laplace transformations.

    I appreciate your help!
  5. Nov 27, 2011 #4


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    Staff: Mentor

    Hey, glad to help :smile:
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