Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: There's work, and then there's work



Chuck Britton wrote:

Superconductivity gets rid of R, but R is only the real component of
the complex impedance!

OK, but remember that the real part is responsible
for the dissipation.

> The L and C components of the impedance create an LC circuit which
> oscillates and radiates the 'missing' 1/2 CV^2.
That is somewhat mixing two ideas.
-- Yes, there is inductance.
-- Yes, there is radiation.
++ No, they are not synonymous.

Consider, for example, a toroidal inductor.
Lots of inductance, negligible radiation.

Consider, for example, an ideal antenna.
Its two-terminal effective impedance is
purely real, purely ohmic, non-reactive.

Every circuit DOES have a finite (and measurable) inductance L.

And perhaps more to the point, a finite
radiation resistance. In many cases, though,
it is possible to arrange that the radiation
resistance is negligible compared to other
losses.

==========

It may be helpful to think in terms of timescales.
-- There is an RC timescale, where R includes
radiation and other dissipative processes.
-- There is a sqrt(LC) timescale.
-- There are other timescales, such as the
switch-closing timescale. When you decide
to start charging your circuit, the switch
has to transition from Rsw=huge to Rsw=small,
and it can't do that instantaneously.
-- etc.

If the RC timescale is long compared to the sqrt(LC)
timescale, the circuit will oscillate. In this case
it is _not_ generally true that the energy dissipated
in the resistor during a charge/discharge cycle is
equal to the energy drawn from the constant-voltage
source; see e.g. the patent cited in my previous note.

A lot of famous textbooks get this wrong.