Partial Derivatives (Uncertainty)

niteshadw

I'm trying to find the uncerainty for the following equation:

e = Qd/AV, where Q is the charge in C, d is the distance in m, A is the area (Pi * r^2), and V is the voltage.

I get something like

delta_e = delta_Q/Q + delta_d/d + delta_A/A + delta_V/V but when I do that, I get a rather large uncertainty number that does not make sense so I think I got hte equation incorrectly....

The lab is based on capacitance and dielectrics...and e in his case is the permittivity of air, lexan, etc..that need to be calculated...

CarlB

I've not seen this sort of problem assignment before, but I would try looking at uncertainty, at least for small uncertainties, as a differential.

The uncertainty in U = AB/C would be:

dU = (B/C)dA + (A/C)dB - (AB/C^2)dC.

Note that each of these is a signed error amount, so if you want the total (absolute) uncertainty, then you need to instead use:

|dU| = |B/C|dA + |A/C|dB| + |AB/C^2|dC

To verify these relations, you can try using small values for the errors and substituting. In fact, if your errors are large, you will get a more accurate value by direct substitution rather than using the approximate calculus equations given above.

Carl

big man

Yeah do it the way Carl said, because the way you're doing it is going to significantly overestimate the associated uncertainty. However, I can see why you got such a high value because the formula you are using is:

e'/e = Q'/Q + d'/d + A'/A + C'/C

Where the ' signifies the uncertainty delta. So what you would need to do is multiply your initial result be "e" to obtain the uncertainty value.
But instead of using that method use the method outlined by Carl.