What happens to current in a circuit if the voltage is halved and the resistance stays the same?

the current doubles..

explanation:V=IR hence I=V/R which means that when the supply voltage is constant ,current is inversely proportional to resistance.thus the current doubles.

practically speaking when the resistance of the load(fan ,bulb,refrigerator,....) is less ,it draws more current from the source so as to balance the voltage across it.i.e; to maintain the voltage across it as constant.

This answer is absolutely correct if you assume that the current comes from a pure voltage source ( voltage source with zero internal resistance). At the other extreme you could have a current source (such as a very large voltage source in series with a very large resistor), and then the current is practically independent of changes if the external resistance is changed (because the change represents a relatively minute change in the overall resistance). With appropriate circuitry it is possible to devise a situation where the current is practically independent of the changing resistance.