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What is the capacitance of the circuit problem.

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data
    An LC circuit consists of a 1mH inductor. The capacitor is fully charged. After 2.1 ms,
    the energy in the capacitor is ½ of its original value. What is the capacitance of the
    circuit?


    2. Relevant equations
    (Q/C)+ L(d^2Q/dt^2)=0

    d^2Q/dt^2= -(1/LC)Q


    3. The attempt at a solution

    I found the above equations in my physics book but I don't know what Q would be (it says that the capacitor is fully charged but it doesn't give an actual number), or how to get into a C= ? format in order to find the capacitance. Also I'm not even sure these are the formulas I need for this problem and if they're not then I have no idea what to do.
     
  2. jcsd
  3. Dec 2, 2009 #2
    Re: capacitance

    you can try to solve the task using Thomson's formula T=2*П * root of L*C
    as i understood there is given that after 2,1 ms the capacitor is half discharged and it means that it will be fully dischardged after 4,2 ms, that is 4,2*10^-3 s - it is full period of time.
    transforming the formula C= (T^2) / (2^2 * П^2 * L) and the result is 4,4 micro farads.
     
  4. Dec 2, 2009 #3
    Re: capacitance

    The charge varies with time according to a cosine function - Q=QoCos(wt)
    w is the angular frequency.
    From the fact that is 1/2 from the maximum at t=2.1 ms you can find w.
     
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