An ideal battery is connected across a resistor of resistance R ....

For an ideal battery, the potential difference $V$ across the resistor remains constant and is equal to the electromotive force of the battery.

The power dissipated in the resistor is given by $P = \dfrac{V^2}{R}$.

Since $V$ is constant, $P \propto \dfrac{1}{R}$.

Therefore, when the resistance $R$ is decreased, the power dissipated $P$ will increase.