I have seen similar questions in the forum but they fail to be very specific . I would ask the question from the viewpoint of Problem Solving. Let me put this question from a textbook :
A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be?
Now from Ohm's Law, $R \propto l $, where $l$ is the length of conductor. So, since length is halved, $R$ is halved.
Since there is no mention in the question that the supply is Voltage Limited or Current limited, I assumed that the supply is a standard household supply which is voltage limited and I used the Relation $P=\frac{V^2}{R}$ and the fact that Heat generated is $H= P\cdot t $, where $t$ is time.
I got my answer correct which is,
The heat generated would be doubled
Now, the real question begins: What if we used the relation $P=I^2 R$, assuming supply to be current limited? Then the answer would be:
The heat generated would be halved.
Why such a contradiction arise? Is my assumption correct or is there some mistake that just somehow lead to a right answer ?