Alan,

John Popelish got a good start with "e is a natural constant that has
some very sweet
properties in many applications of mathematics, and simplifying..."



Then, it looked as thought John Jardine was going to steal my thunder with
"the voltage knows nothing about how it's "supposed" to behave. "



This could resolve to a mater of faith Alan.



Indeed, the voltage/current "knows" nothing.



After observing what happens in such circuits, "we" (those who must
understand all things) very carefully examined what was going on and
"discovered" that there were mathematical expressions or equations which
would model what happens in nature. "We" came up with theories about what
was going on and what was causing it to happen. "We" then found ways to
make the math fit reality. In the case of time constants, we have a natural
phenomena which is very nicely described by the equations stated elsewhere
in this thread (the 1/e thingy). It is just like the F=MA equation. "We"
discovered that the force applied to a mass is equal to the mass times the
acceleration. The Mass knows nothing about force, acceleration or
mathematics. We found that this math describes nature.



It is exactly like a model airplane (or whatever). We make the model to
look like the real thing. The real thing knows not of the model that we
built, but if we did a good job, I or you can now look at the model and
"know" just how the real thing looks.



The math behind all of our sciences is just like this. *WE* found math
which models reality and because we did such a good job, we can now "do the
math" and "know" how the real thing should behave.



To be a little more specific, in the case of the time constant. we have
theories about current flow, charge, capacitance, inductance magnetism and
resistance which are borne out by countless experiments and then by
subsequent usage. These theories have all had mathematics fitted to them,
and by golly everything fits. We can now plug-in values to equations till
the cows come home and holy-cripes! The real thing does just what the math
predicted. Based upon the properties we have observed for each type of
component, this math works out such that this 1/e thingy fits just right.



In other words, the answer is: "It just does!"

73,
--
Steve N, K,9;d, c. i My email has no u's.




"Alan Horowitz" wrote in message
om...
when a current just starts flowing into a RL or RC circuit, how does
the voltage "know" that it should be increasing exactly 63% during
each time-constant period?

And whence the number 63%?