Ohm's Law and Battery Life
Date: 08/18/99 at 17:04:12 From: Scott Stongle Subject: Ohm's law If you have a 12 V battery that has 275 cold-cranking amps and you put a load of 12 V at 7.2 A on it, how long should that battery run the load? Also, I was wondering if I need to figure the resistance of the system before I can complete the calculation. Thank you.
Date: 08/23/99 at 11:04:20 From: Doctor Douglas Subject: Re: Ohm's law Hi Scott - Thanks for writing. Let's see if the following helps. Using Ohm's law, Voltage = Current * Resistance: 12 V = 7.2 A * R So the resistance of the load is 12 V/7.2 A = 1.67 Ohms. We've just figured out the resistance of the load. There is also an internal resistance of the battery that limits how much current it can supply, even to a short circuit. This limit is the 275 amps (the maximum current that can be drawn). So the internal resistance of the battery is given by: 12 V = 275 A * [R_battery + R_short] = 275 A * [R_battery + 0] = 275 A * R_battery Now we have R_battery = 12 V/275 A = 0.0436 Ohm, which is small indeed. If the load is smaller than about 10*R_battery, then the battery will not have enough oomph to put out 12 V into a load that small. Now since our load (1.67 Ohms) is bigger than R_battery, there's no problem so far - the battery will put 12 V across the load and be able to deliver the 7.2 amps, which is much less than its maximum rating of 275 amps. Now let's see if there's enough information to answer your question, "how long will it run the load?" The property of the battery that you need to know here is known as its "capacity," and this expression is usually given in units of ampere-hours. This capacity is illustrated by the difference in battery sizes: a D-cell (flashlight) and a AA cell (Walkman) have the same voltage (1.5 V), and probably very close to the same R_battery, but the D-cell has much higher capacity (and hence is bigger and heavier, because it can last longer) than the AA. As you might imagine, if the load is smaller it will require more current and the lifetime of the battery will be smaller. In your question, we don't have this information on the battery capacity, so at this point we can't yet answer how long it will last. If you find out the battery capacity, then you can calculate the lifetime from lifetime = (capacity) / (load-current) assuming that everything remains constant. Of course, real batteries and real loads might behave slightly differently, and this could make things a bit more complicated. Hope this helps! If you are still unclear about anything, please write back. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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