Re: Resonant Frequency

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Hi Ed,
> The self resonant frequency is 263 khz.  The quarter wave
> frequency calculated for a 1604 foot long wire is 146 khz.  So 
> why does this come out backwards from what I expected?

> I would have guessed it would have been lower due to the added
> self capacitance of the solenoid secondary.

Your expectation is quite reasonable, the extra capacitance does
lower the frequency by a large factor.  Working against this is the 
mutual inductance between remote parts of the wire, which increases
dramatically when wound up.  This raises the 'velocity factor' by a
huge amount, (*) more than offseting the effect of increased C, at
least in a solenoid.  We're getting hints that the balance may be
shifted the other way in flat coils, but we've a way to go yet on
that.

(*) points that were X metres apart in the straight wire, are
brought to within pitch * X/(2.pi.radius) metres, thus giving the
increase.  This is usually so close that we can neglect retardation
and work instead with the abstractions of 'inductance' and
'capacitance' rather than the B and E fields.
--
Paul Nicholson
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