1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted