Re: funny capacitor

["John S. Denker" <jsd@MONMOUTH.COM>]

At 12:25 PM 3/9/01 -0500, Ludwik Kowalski wrote:
> 1) A rock is dropped from a roof. How long does
> it take to hit the ground? 3 seconds. Is this the
> "one and only one reproducible solution?" I think so.

Sure.  A measurement of (delta t) is a well-posed question with a unique
answer under the stated conditions.

> But somebody may object saying that there are many
> solutions. One is when my stopwatch is initially at zero,
> another when the initial time is 10 seconds (and final
> time is 13 s), etc.

Different question, different answer.  Asking for the arrival time is
different from asking for the duration of flight.

> 2) Consider a common capacitor. Suppose its geometry
> is such that C=100 pF. What is Q when dV=10 V? It is
> 1000 pC. Is this the "one and only one reproducible
> solution?" I think so.

The capacitance is a gauge-invariant number.

The Q(V) problem is well-posed, and has a unique answer,
if all the Vj are specified.  I've said this N times now.

> But somebody may object saying that there are many
> solutions. One is for V1=0, V2=10, another is for
> V1=50, V2=60, etc. Any set of two voltages is a
> solution provided V2-V1 = 10.

Different question, different answer.
The unrestricted V(Q) problem has a goodly-sized solution set.

Various questions about (delta V) are well posed and have unique solutions.
Different questions have different answers.

> 3) JohnD was saying that the well defined V(Q) problem
> (find V1, V2 and V3 when Q1, Q2 and Q3 are given) has
> many solutions. How does this differ from the "many
> solutions" claims in the first two items above?

It differs according to the rule:  "Different questions, different answers."