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RE: Induction heating in toroid / short circuit of secondary



Hi Colin,
              My comments (just couldn't keep quiet :(


> 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.  

That suggests to me that superconductors lose power ??
 
> 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!

The primary heats up in meeting the reflected load current but the 
secondary, if it is perfectly conducting  ??   If both coils conduct 
perfectly, then the source alone cops the extra heating (unless it too 
has zero resistance). (Y-N)?

> 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).  

I cannot agree that load current will cause a transformer core to 
saturate. A reduction in reflected load resistance will make it looks 
as though it does. Consider that if the load is heavy enough, pri and 
secondary flux cancel leaving a lump of iron with little flux in it. ?
 
> 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?

Agree with the last sentence on condition that RMS current is small 
if the toroid conductance is less than perfect. 

Regards,
Malcolm