Does Ohm's Law still apply when the total number of Amps is limited?

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Simfish
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As in, what if you have a VERY high voltage? Then I = V/R.

But what if you only have a limited number of charge carriers that could eventually run out? Then what will happen to the current? Will it suddenly stop following Ohm's Law? Will it immediately drop off to 0, or gradually drop off to 0?
 
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You can't have high voltage without enough charge being separated, so when you run out of charge carriers, you run out of high voltage as well.