Associated Topics || Dr. Math Home || Search Dr. Math

### 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
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.

"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

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/
```
Associated Topics:
High School Physics/Chemistry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search