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RE: Induction heating in toroid / short circuit of secondary
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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