Final answer:
The gradual dimming of car lights indicates that the battery output voltage decreases as the battery is depleted, which can be caused by increased internal resistance and slowed chemical reactions. If both the battery light and parking brake light come on, it may point to an electrical system malfunction.
Step-by-step explanation:
When the car lights are left on and the battery runs down, they slowly dim instead of suddenly turning off because the battery output voltage decreases as the battery is depleted. This effect is due to the fact that all voltage sources have an energy source and an internal resistance. As the battery discharges, the internal chemical reactions that produce electricity slow down, and the internal resistance increases, both of which cause the output voltage to drop.
This is related to why the battery light and the parking brake light may come on in your car. The battery light usually indicates that the car's electrical system is not charging properly, possibly due to a failing alternator, loose or corroded battery cables, or a deteriorating battery itself. The parking brake light can indicate that the parking brake is engaged, but if it comes on simultaneously with the battery light, it could suggest a potential electrical system issue.