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Re: Induction heating in toroid / short circuit of secondary
I think what "saves" us is that dFlux/dt becomes greatly diminished due
to the large circulating current in the shorted toroid: most of the flux
is deflected per, as you properly point out, Lenz's Law. As to the
similarity to a shunted transformer...hmmm...I suspect that the
flux-leakage path existing between primary and secondary is so large a
factor that additional shunting by the toroid is minimal. Just a guess,
of course.
On Wed, 22 Dec 1999 03:03:15 -0700 Tesla List <tesla-at-pupman-dot-com> writes:
>Original Poster: Colin Dancer <CMD-at-datcon.co.uk>
>
>Thanks for the spelling corrections :-).
>
>I'm also almost convinced that the power lost is minimal, but I think
>the analysis might be more complex than you suggest.
>
>Try this for size....
>
>As far as I remember, Faraday's law of induction indicates that the
>EMF generated in a coil is equal to the number of turns in the coil
times the rate of change of flux through the coil. To a first
approximation, the current in a toroid is therefore given by (dFlux/dt)/R
and power lost as (dFlux/dt)^2/R.
>
>So as the resistance goes _down_ the power lost goes _up_, and
>vice-versa.
>
>This makes intuitive sense as at one extreme a ring of insulating
>material would have a very high resistance and a very low power loss,
and at the other extreme we all know what happens if you short the
secondary winding of a normal transformer!
>
>As you say, however, Lenz's law means that the induced current will
>set up an opposing magnetic field which will tend to reduce the rate of
change of flux.
>
>For a tightly coupled transformer (i.e. iron core) this will result in
>a reduction in the inductance of the primary, which will in turn result
>in an increased primary current flow, which in turn return will restore
>the rate of flux change to its original value (up until the point where
the core saturates).
>
>In a loosely coupled system (such as between the toroid and
>primary/secondary in a tesla coil) there will be some increase in
>primary current but, as you suggest, some of the flux will be forced
>round the side of the toroid. In that case, I think peak power will be
>at a maximum when the toroid's electrical resistance means that the
>induced current causes the effective magnetic resistance of the >area
inside the toroid to match the effective magnetic resistance of >the
alternative path round the outside.
>
>I believe this is exactly equivalent to the current limiting in a NST,
>where the shunts provide an alternative magnetic path which doesn't
>pass through the secondary coil.
>
>I haven't done the maths, but I suspect that the loose coupling >means
that a low resistance toroid will dissipate very little power.
>
>Views anyone?
>
>Colin.
>-----Original Message-----
>From: Tesla List [mailto:tesla-at-pupman-dot-com]
>Sent: 21 December 1999 18:33
>To: tesla-at-pupman-dot-com
>Subject: Re: Induction heating in torroid / short circuit of
>secondary
>
>
>Original Poster: Kennan C Herrick <kcha1-at-juno-dot-com>
>
>Here is a thought on the subject:
>
>A "shorted" toroid constitutes a single shorted turn adjacent to the
>secondary. There will be a circulating current in it but the power
>it
>might subtract from the system will be very small since its resistance
>is
>very low ((I^2)R--remember?). Its only deleterious effect might be
>to
>set up its own magnetic field that would be in opposition to the field
>of
>the secondary--tending to push aside that latter field. Apparently
>that
>doesn't happen to any great extent, or else if it does, it doesn't
>matter
>all that much, at the top end of the secondary coil where that
>magnetic
>field is the weakest. Or else--the field tending to be pushed aside
>merely "sneaks out" between the secondary and the toroid. That it
>might
>be deflected from passing completely thru the toroid is of no
>consequence, of course, since the purpose of the toroid is not at all
>to
>act as a part of the transformer per se.
>
>And by the way, everyone--and please no one take offense: It's
>"toroid"
>with 1 "r" and it's "dielectric" with an "e" and not an "a".
>Sorry--I
>can't help it!
>
>Ken Herrick
>___________________________________________________________________
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>
>
___________________________________________________________________
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