A car owner forgets to turn off the headlights of his car while it is parked in his garage. If the 12.0-V battery in his car is rated at 51.0 A · h and each headlight requires 27.0 W of power, how long will it take the battery to completely discharge?

22.6 hours

Explanation:

The power is the measure of the rate of energy.

In this problem, the 12.0 V battery is rated at 51.0 Ah, which means it delivers 51.0 A of current in a time of t = 1 h = 3600 s. The power delivered by the battery can be written as

where

I is the current

V = 12.0 V is the voltage of the battery

So the energy delivered by the battery can be written as

Where

So the energy delivered is

At the same time, the headlight consumes 27.0 W of power, so 27 Joules of energy per second; Therefore, it will remain on for a time of: