Introduction:
When a resistor is connected to an ideal battery, it experiences a flow of electric current. This current generates heat in the resistor, causing power to be dissipated. The amount of power dissipated can be calculated using Ohm's Law and the formula P = I^2 * R or P = V^2 / R, where P is power, I is current, V is voltage, and R is resistance.

Effect of Decreasing Resistance:
When the resistance of the resistor is decreased, it means that the value of R becomes smaller. This has a direct impact on the power dissipated in the resistor.

Increased Current:
According to Ohm's Law, when resistance decreases, the current flowing through the circuit increases. This is because the voltage across the resistor remains constant (as long as the battery is ideal), but the decrease in resistance allows more current to flow. Therefore, decreasing the resistance results in an increased current.

Increased Power:
Since power is directly proportional to the square of the current, an increase in current leads to an increase in power dissipated in the resistor. This is because the power formula P = I^2 * R shows that power increases exponentially with the increase in current. Therefore, when the resistance is decreased, the power dissipated in the resistor increases.

Conclusion:
In summary, when the resistance of a resistor connected to an ideal battery is decreased, the power dissipated in the resistor increases. This is due to the increase in current flowing through the circuit, which results from the decrease in resistance. Therefore, the correct answer is option A) increases.

B, because power is inversely proportional to resistance