[MichaelDay]

dark, changing to an underdrive pulley will exacerbate your charging problems. You have multiple problems. First, if the lights are dimming when the bass hits indicates that the peak power demands of your system require a cap. The capacitor is designed specifically for that problem by providing the extra power needed during those milliseconds of bass peaks. Secondly, if you use the stereo much while the engine is off or idling, the starting battery isn't good for extended high current demand without the engine running at a high enough speed to let the alternator provide the required energy to keep up with the load. A deep cycle battery will survive being drawn down and recharged MUCH better than typical starting batteries. Third, your alternator may not be up to the job you are asking it to do and certainly adding an underdrive pulley is the WRONG direction as it will reduce alternator output at lower engine speeds. Fourth, your grounding and or wiring may not be adequate to support the power demands being placed on them even if they were professionally installed.

To answer your original question, your engine develops a fixed amount of power. You can use this power to EITHER move the vehicle faster or to generate more charging current to drive HID's or high powered stereo or any additional electrical loads.