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Default Rewinding a transformer

Unwound the wire off the primary and know the exact length,L. Also the
bobbin dimensions of course. The wire I have around, is a slightly
smaller diameter ,d2, original d1. Would the rewind length , for the
approx same number of turns,be simply L * (d2^2)/(d1 ^2)ie shorter by
the ratio of areas or some other consideration like packing factor
change, assuming current carrying capacity is sufficient.
I know I should have counted off the turns but I assumed there would be
a "welded" mess of metal in the middle, and would have to rely on weight
of the wire.
 
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