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Internal resistance.

The ideal current source has no internal resistance in parallel with it (if it was set to supply no current it would act as an open circuit), and all the current it supplied would have to flow through its load (even if the load was an open circuit, in which case the voltage across the current source would be infinite).

A real current source has the practical limitation that it must have an internal resistance in parallel with it, therefor some of the current it supplied is bypassed through that internal resistance and never reaches the load (if the load was an open circuit, then all the current supplied is bypassed and the resulting voltage drop across the internal resistance limits the voltage across the current source).

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