An energy source will supply a constant current into the load if its internal resistance is
zero
non-zero but less than the resistance of the load
equal to the resistance of the load
very large as compared to the load resistance
If r=0, then I=E/R that means current will be constant for a given load.
But if we talk about a general case, then if internal resistance is very large as compared to the load resistance, then we can neglect the load resistance in every case and the equation will become, I=E/r.
So for general case, we can say that internal resistance should be very large as compared to internal resistance for current to be constant
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