----- Original Message ---- From: Christoph Pacher <christoph.pacher@arcs.ac.at> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, January 4, 2008 11:44:17 AM Subject: Re: [math-fun] xkcd points out dangers of math fun Fred lunnon wrote:

Thinking about this, though --- what happens in the original problem if we replace "1 ohm" by "1 microF" ?

Presumably probabilistic simulations _do_ depend in an essential way on the resistances being real?

There should not happen much. The impedance of an (ideal) capacitor is Z=-i/(2 pi f C). The -i corresponds just to a phase shift of Pi/2 between voltage and current and can be ignored for the moment. 1/(2pi f) is a constant factor which you take out now and plug in at the end (if you are interested in the impedance and not the capacity). Thus you basically replace 1 Ohm with the inverse of 1microF in the "standard calculation" and take the inverse at the final result again. How you obtain the standard calculation (probabilistic or not) is of course not important. Christoph _______________________________________________ Yes, that's completely correct. The effective resistance between two nodes in the resistor network is a homogeneous function of degree 1 in the individual resistances. When all the resistances are equal, Reff = k R, for some positive constant k. If R is replaced by an impedance Z, then Zeff = k Z. Gene ____________________________________________________________________________________ Looking for last minute shopping deals? Find them fast with Yahoo! Search. http://tools.search.yahoo.com/newsearch/category.php?category=shopping