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LRC Circuit with large resistance

  1. Dec 3, 2011 #1
    1. The problem statement, all variables and given/known data

    (The τ's are the capacitive and inductive time constants, Q = qmax)
    In an LRC circuit with large resistance, show that as t → [itex]\infty[/itex], q → 0.
    When t = 0, q(0) = Q. When t = τL, q(τL) = 2Q(1+e)-1cosh(τLC.

    Show that q(t) = (Q/1+e)e-t/τC + (Q/1+e-1)e-t/τLet/τC

    2. Relevant equations

    q(t) = Qe-Rt/2Lcos(t[itex]\sqrt{}1/(LC) - (R/2C)2[/itex] + [itex]\phi[/itex]

    3. The attempt at a solution

    I have no idea where to start, other than to write out cosh in terms of exponentials, but still nothing. Because the circuit is not tuned to the resonant frequency, the capacitor and inductor produce reactance.

    Somehow I get the feeling I am missing something that makes this into a simple "plug n' chug" type problem.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
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