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Confusion - Diff Eq for a Circuit? What does my professor mean?

  1. Mar 22, 2010 #1
    1. The problem statement, all variables and given/known data

    My professor wants us to derive a differential equation for the current in a circuit.

    The circuit has a battery with voltage E, resistor with resistance (iR)??, and inductance L. It's in series.

    3. The attempt at a solution

    What REALLY confuses me are these things:

    Why iR instead of R? Is the i supposed to represent current? Then why is it given for the resistance and not inductance? I don't think it could be a complex number.. it just wouldn't make sense.

    Anyway, I assumed she meant R instead of iR. Then I set up a diff eq like this:

    i(t)*R + L(d/dt)i(t) = 0
    after a bit of math, I got
    d(i(t))/i(t) = -(R/L)dt
    and integrating some more math...
    i(t) = Cexp(-(R/L)t) where C is some constant.
    okay, that's fine. It seems to make sense to me

    But then she wants us to solve it if i(0) = 0 and i(t=0) = 0.

    First of all.. isn't she saying the exact same thing twice? i(0) = i(t=0) I'm guessing?
    And second of all... according to my equation, i(0) = Cexp(0) = 0 implies C = 0, or that the whole expression is 0. How do I solve the differential equation if C = 0 exactly? Or does it only have a solution of 0?

    Any clarification could help. Thanks!
  2. jcsd
  3. Mar 22, 2010 #2


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    Homework Helper

    Shouldn't it be

    E = i(t)R+ Ldi/dt
  4. Mar 22, 2010 #3
    ah, okay. that makes more sense. I should be able to figure something out - thanks!
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