A Charge/Current Problem - Solution

        You have an application using an instrument that needs 12 volts (nominal voltage).  The instrument is remote from a power outlet.  Every hour, on the hour, it turns on for ten minutes automatically.  When it is on it draws 75 milliamperes.  You have several options on batteries.

Option A.  Buy some alkaline batteries and put them in series to get the required voltage.  Each alkaline battery has a nominal voltage of 1.5 volts and you will need eight batteries to get 12v.  Each battery stores .75 ampere-hours and costs $1.01.  If you buy 10 to 24, the price drops to $.85 each.  Above 25 the price is $.54.

Option B.  Buy a twelve volt battery with .75 ampere hour capacity that costs $10.00.

Option C.  Buy a rechargable nickel-cadmium battery.  A 12.2 volt battery with .45 ampere-hour capacity costs $67.82.  With a recharger you can recharge one in two hours.

        Determine which option is best and explain your decision so that a non-Electrical Engineer can understand your explanation.

Solution

        You need to determine how much charge is required.

Option A

The instrument draws 75 mA (or 0.075 A) for ten minutes (600 sec.) every hour.  That's .075A * 600 = 45 coul.  In ampere-hours, that's 45/3600 = .0125 A-hr, so one of these batteries will last for .75/.0125 = 60 hrs or 2.5 days.  Since the best price is $.54/battery, that's going to cost you $.54*8/2.5 each day, or $1.728 a day.

Option B

Since this battery has the same number of ampere hours as the batteries in Option A, you're going to spend $10/2.5 = $4 a day.  That's more expensive than option A.

Option C

This battery has a lower ampere hour capacity, so - after a charge - the battery will last .45/.0125  = 36 hours or 1.5 days.  If you buy two batteries, you can do it for twice the $67.82 or $135.64.

        One question is how long it would take you to spend that much using Option A.  That would be 135.64/1.728 or 78.5 days.  So, if you're going to run this thing longer than two months, it will pay you to buy the rechargeable batteries - Option C.  That assumes you have a charger.  If you don't have a charger you have to factor that in as well.