Re: dielectric constant

[John Denker <jsd@MONMOUTH.COM>]

At 01:24 AM 1/31/01 -0800, Michael Bowen wrote:
> What's a cheap and easy way to measure the DC (or zero-frequency, for
> purists) capacitance to within 5% or so for a beginning class? Or, how
> do you do it even if your method isn't cheap and easy?


1) If "zero frequency" is shorthand for "low frequency", then there are
lots of ways to measure capacitance at low frequency.  Perhaps the most
common is a bridge circuit, where one side of the bridge consists of the
unknown capacitance in series with a known, reference capacitance.

2) If "zero frequency" really means zero frequency, then there are two
possibilities:

2a) Suppose we view the capacitor as a two-terminal device.
 -- This is the viewpoint that electrical engineers take.
 -- This is the viewpoint that is a prerequisite for applying
    Kirchhoff's laws and the approximations implicit therein.

In this case, there is no such thing as DC capacitance.  Capacitance is an
AC-circuits concept.  Specifically, if we use the operational definition C
= Q / V, then
 *) We can measure the DC voltage on the capacitor terminals.
 *) OTOH to measure Q requires taking it out of the capacitor.  This
requires a current.  If the total Q is to be finite, the current cannot be
constant for all time, i.e. it must have an AC component.

2b) Suppose instead we are allowed to poke around in the innards of the
capacitor.  This is extremely inconvenient for ordinary practical
capacitors;  if you really want to do this you ought to use a capacitor
designed for the purpose.  In that case, the procedure for measuring the DC
capacitance is so dependent on the architecture of this specialized
capacitor that it is hard to make generalizations.

At this point I have to ask, why would anybody ask about the DC
capacitance?  If I knew why they cared, I might be able to design an
apparatus that more directly measures whatever quantity they really care about.