The \(12-V\) automobile battery in Figure \(\mathrm{P}_{1-10}\) has an output capacity of 100 Ah when connected to a head lamp that absorbs \(200 \mathrm{~W}\) of power. The car engine is not running and therefore not charging the battery. Assume the battery voltage remains constant.
(a) Find the current supplied by the battery and determine how long can the battery power the headlight.
(b) A 100-W device is connected through the utility port. How long can the battery power both the headlight and the device?