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Current calculation of passive RLC network using DE

Discussion in 'Electronic Basics' started by Mike, Jun 25, 2007.

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  1. Mike

    Mike Guest

    Hi Experts,

    Not entirely sure if this posting is more appropriate in the symbolic.math
    group or this group, but since it is a current calculation, I'm thinking its
    fine to post here as well. I am trying to figure out how to solve the
    following problem relating to a passive circuit in a closed loop described
    by the following differential
    equation:

    L*dI/dt + R*I = Eo (intial Differential Equation)

    The problem is to solve the equation when an initial current Io is flowing
    and a constant emf Eo is impressed on the circuit at time t =0. Using
    variables separation, I can arrive at:

    dI / (Eo - R*I) = 1/L*dt

    and then I integrate both sides:

    -log(Eo-R*I)/R = R/L*t + C1 // note - only 1 log term

    The published solution using the initial condition I(0) = Io is:

    log(Eo-R*I) = R/L*t + log(Eo - R*Io) // note the 2nd log term

    I am guessing that the additional log term is obtained by solving for the
    constant C1, but how ?

    Any input would be greatly appreciated!

    Thanks,
    Mike.
     
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