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I was thinking about measuring the voltage over the coil, but I'm not sure how the voltage relates to the current for this coil.
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I think your on the right track right there. Test the resistance of the coil outside the circuit. (I assume your designing this or that you can remove it, test it, and put it back in.) Once you know the resistance,
that is how the voltage relates to the current. It's a coil, so it has special AC properties, but when the current is stable (DC) it acts just like any length of wire or any resistor.
(For the most part, that is. If you need to be precise you could actually put various different volatges across it and measure the current to see if is linear enough for a simple resistance value to be reliable. All this done outside of the circuit.)
Edit: I think I remember being told that a uniform length of wire is very close to an ideal resistor. Is that true? Does anyone know? :endEdit
Once it's back in the circuit, you just measure the voltage like you said.
--tim
Also I did look briefly at Hall Effect sensors an they are quite small, some are cheap (a couple bucks or so), but some are designed for sensing position. (Like the position of a magnet) They don't provide a numerical output. (The ones I saw) And they won't be set up specifically for your coil. However the
leads to your coil which carry the same current might be something more standard that can be measured with an off-the-shelf chip. (You would have to do some research and see what you find.) You'll would also have to make some room and extend the leads to the coil so that the sensor can sense just that and is not affected by other components. (Even though the sensor itself is small.) Did not know such a thing existed.. Cool.
But, I think my further above suggestion makes more sense.