Wireless Electricity: Replicating MIT's Witricity on Smaller Scale

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rburns
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I'm trying to replicate MIT's "Witricity", but on a smaller scale. I have a coil connected to a function generator and then a second coil (with more loops than the first) connected to an LED. So I guess now I have a transformer. And the LED lights up when the coils are up to 10cm apart. I would like to get more distance - so I think I need to match the resonant frequency of the two circuits, but I'm not sure how. I think I need to put a capacitor in each circuit and use F=1/[2(pi) *sq rt(LC)], to find the resonant frequency, but how do I measure the inductance of each coil? Thanks for any help!
 
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Will you please describe your coils a bit more?
 
The first coil is about 6 inches in diameter with 30 loops and the second is about 5 inches in diameter with about 40 loops.