How do you measure the value of an unknown inductor? If you have an LCR bridge or meter, you are probably going to use that. If not, there are many different techniques you can use. All of them rely on the same thing my Algebra teacher Mr. Harder used to say back in the 1970’s: you have to use what you know to get what you don’t know.
[Ronald Dekker] must think the same way. He took a 50-ohm signal generator and a scope. He puts the signal output to about 20kHz and adjusts for 1V peak-to-peak on the scope. Then he puts the unknown inductor across the signal and adjusts the frequency (and only the frequency) for an output of 1/2 volt peak-to-peak.
The idea is that the magnitude of the inductive reactance at the half-way part must be 50 ohms (forming a 50/50 voltage divider with the source impedance). [Ronald] does the math derivation in detail, but it works out that the inductor (in uH) is 4570/f where f is the frequency in kHz. In reality, the setting of the 1V reference is not completely necessary, but it simplifies the way he does the measurement if you read the full post.
Of course, there is probably some stray resistance in the circuit, but not enough to make much difference in most inductors. If you have reason to suspect otherwise, [Karen Orton] contributed the math to get to a slightly more complex expression that lets you factor the DC resistance of the coil in your calculations.