Re: capacitance formula

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "by way of Terry Fritz <twftesla-at-qwest-dot-net>" <Mddeming-at-aol-dot-com>

In a message dated 9/16/02 2:08:42 PM Eastern Daylight Time, tesla-at-pupman-dot-com
writes:


>
> Caution is the order of the day here folks: I am
> fairly certain that (ENGLISH OR METRIC) distance units
> MUST be used for the measurement units, or this gives
> an incorrect answer. Found this out a long time ago
> when my capacities didnt jive using inches for the
> length and area factors. Although it sounds a little
> illogical, we CANNOT ASSUME that just because we have
> converted BOTH the numerator and denominator to a
> different ratio of length standard, (ie 2.54 cm = 1
> inch); that converting both the top and bottom length
> factors will also convert the ratio answer to be
> identical. This can easily be shown for a case example
> of A=1 inch^2 and d= 1/2 inch which easily computes
> that A/d ratio to be 2. Now convert to metric and find
> the A/d ratio; this becomes 2.54^2/1.27 using cm or
> A/d = 5.08, not the no 2 that was arrived at using
> inches as the length factor. Thus this formula was
> derived SPECIFICALLY FOR METRIC MEASUREMENT LENGTHS,



The problem is that one cannot plug numbers blindly into a formula without
regard to what they represent. However, many of those who were raised with
calculators tend to ignore dimensional analysis. If one considers the
dimensions and not just the numbers, it is immediately obvious that you get the
same VALUE for A/d in both your examples.

      1 in x 1 in / 0.5 in =2 in. likewise, 2.54 cm x 2.54 cm / 1.27 cm = 5.08
cm

While 2 does not equal 5.08, nevertheless and A/d ratio of 2 inches is
IDENTICAL to an A/d ratio of 5.08 cm. One would expect the ratios to be the
same number IF AND ONLY IF they were pure, dimensionless numbers, not numbers
with dimensions attached. Crunching numbers without regard to dimensions will
almost always lead to problems. Even Einstein's famous E=mc^2 looks funny if
mass is in slugs and c is in furlongs per fortnight, but it can be done and the
answer even expressed  in "heat of equivalent standard cartloads of buffalo
chips" ;-) It's all in knowing how to PROPERLY handle the dimensions.

Matt D.