How to Determine the Uncertainty of Q.total?

[blog]

Problem 1
Given: 2 capacitors in a series, each capacitor's farad & voltage across.
Voltage uncertainty 1%, capacitor uncertainty 5%
C1: 1019microFarads C2: 553microFarads
V1: 3.58 volts V2: 6.56 volts
Uncertainty: 5% for CAPs & 1% for Volt

Find Q for each: Q1=3648 Coulombs Q2=3627 Coulombs
Find Q's +/-(variance): SQRT(.05^2 + .01^2) = .051
Q1 Variance: 186 Q2 Variance: 185


Now for the question:
find Q.total Q.total=C.eq * V.total => 3634.84
What is the Uncertainty of Q.total??


Does anyone know how to find Q.total's variance?
I've looked through my text and online, still no luck.

If anyone could make a suggestion, I'd be very appreciative.


Thanks

 

[Jezuz]

Hmm.. you should consult a book on statistics. I think that Gauss proved something about how to calculate the variance.

For example, if you have the formula Q = A * B and you know the variances of A and B, then the variance of Q can be calculated. If I am not mistaken you find it with
Var(Q) = dQ/dA * Var(A) + dQ/dB * Var(B)
and this formula applies generally.

I might have confused the variance with the standard deviation or something so there might be a squareroot over the whole right hand side...