Final answer:
Headlights should be used at night and during poor visibility conditions; a 100 Ah battery can sustain 40 W headlights for a calculated duration, and superconductors could prevent headlights from dimming during engine startup, considering the battery's internal resistance.
Step-by-step explanation:
Headlights should be used in several conditions to enhance visibility and safety while driving. They should be turned on not only during nighttime but also during adverse weather conditions such as fog, rain, or heavy snow. Moreover, many regions have specific laws about using headlights during certain hours or in certain conditions, like when using windshield wipers in the rain.
As for the electrical aspect regarding headlights, a vehicle's 12-V automobile battery rated at 100 Ah can sustain two 12-V headlights, each rated at 40 W, for a calculation of how long the lights will stay on without the engine running. This equation would be solved by dividing the total ampere-hours by the total current drawn by the headlights. If the car has superconductor wires, which have no resistance, the headlights would not dim when starting the engine, as all the power would go to the starter motor, but this is also affected by the battery's internal resistance.
Additionally, headlights typically have a higher initial power draw when cold due to low resistance, which then decreases as the bulb warms up and the resistance increases. The design of headlights sometimes includes a parabolic mirror to focus the light, which is the same principle used for focusing sunlight in solar power generation applications.