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How long till the batteries die?
By Professor Andy Ruina, Mechanical and Aerospace Engineering
Suppose you have two cell phone batteries. They are both fully charged at the start with a charge of 1 amp-hour. Your phone uses 1 amp. Immediately when the first battery is discharged you swap batteries and put the empty one in a charger. It charges at .5 amps. When the second battery goes dead you swap again, putting the second battery in the charger and the incompletely charged first battery back in the phone. You use it until its dead. You keep swapping and charging until both batteries are completely dead.
a. How many swaps have happened then?
b. How long does that take?
c.&d. What are the two answers if you started with 10 batteries?
Assume infinitely fast swaps, batteries that keep their capacity, and so on.
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