# Homework Help: Amplification factor as function of capacitance coefficients - mathematical problem

1. May 31, 2012

### Inertigratus

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