After leaving on my headlights all night, my automotive battery from problem 1 is drained of all its energy. I plan to recharge the battery by connecting it to a battery charger powered by the 120 VAC power outlet in my garage. The battery charger is essentially a 120 VAC to 12 VDC power supply. The charger is 90% efficient at converting AC power into DC power. In other words, 90% of the 120 VAC power that goes into the charger shows up as 12 VDC power. The other 10% of the power that comes in is converted to heat within the charger. If I want to warm my garage, this heat is useful, otherwise it is considered a waste product. Batteries are not 100% efficient. In other words, not all of the energy you put into them during charging can be extracted during discharging. This is because the battery generates heat, and also undergoes some chemical reactions that consume energy. Assume to fully charge the battery of problem 1 you will need the charger to put in 120% of the energy that was extracted during discharging (actual lead acid batteries are probably less efficient than this). Assuming you pay the average rate for residential electrical power in the USA (you will need to look this up, or if you wish, you can use the rate that showed up on the last utility bill you paid). Required:
How much will it cost to recharge your battery?