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Amplification factor as function of capacitance coefficients - mathematical problem

  1. May 31, 2012 #1
    1. The problem statement, all variables and given/known data
    This seems like a fairly simple problem, it is practically an algebraic problem.
    I'm supposed to show that dV1/dV3 = c32/c31
    V1 = constant = 1, V2 = 0
    In a similar problem, it was solved by substituting V3=0 to get Q as a function of V1.

    2. Relevant equations
    Q1 = c11*V1 + c12*V2 + c13*V3
    Q2 = c21*V1 + c22*V2 + c23*V3
    Q3 = c31*V1 + c32*V2 + c33*V3


    3. The attempt at a solution
    I tried taking derivatives of all Q with respect to all V, substituting V2=0 and doing all sorts of things and I can't show what is asked to show. However, the relation that I'm supposed to show is true only if c21=c31, if my calculations are correct. I have no idea how to show that that's indeed the case though. I would appreciate it if you have some hint or idea.
    Basically what I have now is the following:
    µ = dV1/dV3 = dQ3/dQ1 and c32/c31 = dQ2/dQ1 so they are equivalent if dQ2/dQ3 = 1 which is equivalent to c21=c31.
     
    Last edited: May 31, 2012
  2. jcsd
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