A current of 0.25A flowing through a bulb at 12V results in a power output of 3W, calculated using the formula power equals current times voltage. To find the resistance of the bulb, Ohm's Law can be applied, where voltage equals current times resistance (V = IR). Rearranging this formula gives resistance as voltage divided by current, which in this case is 12V divided by 0.25A, resulting in a resistance of 48 ohms. The discussion emphasizes understanding the relationship between power, current, voltage, and resistance in electrical circuits. Mastery of these concepts is essential for success in physics.