Resistance R is connected to a ideal battery. Internal resistance of an ideal battery is zero. So it provides constant potential difference between two terminals.

Power dissipated by the resistor is given by

Power,

Where

V is the voltage or potential difference

R is the Resistance of the resistor

Power P is inversely proportional to Resistance R. If the value of R is decreased, the value of power P will be increase.

A resistor R is connected to an ideal battery. If the value R is decreased, the power dissipated in the resistor will increase. So option A is correct.