Problem dealing with mAH, mA, and volts

[adc85]

Suppose the current drain (on average) of a LED is 2mA at 4.5v. Now suppose that 250 mAH 1.5v cells are being used to power this thing. I want to keep this LED powered for 504 hours (3 weeks), how many cells are needed and how should they be arranged?

Now, here is my stab at the problem.

There is a voltage requirement of 4.5v, right? So, place 3 1.5v cells in a series to add the voltage up to 4.5v. So far I know that there will be a series of 3 cells.

There is a mAH requirement of 250 mAH, right? So there will be cells in parallel to each other to meet this requirement (since putting cells in parallel adds current). At this point, I get stuck, because I am not sure how to compute how many I will need in parallel.

I do know that battery life = capacity / current though...

Any help?

 

[adc85]

Anyone know?

 

[Office_Shredder]

So now that you have a set of three batteries in parallel, you need to see how many of those you need.

As a hint, you need 2mA for 504 hours. So try multiplying that. See what units you get.

 

[adc85]

So you get 1008 mAH. Each cell's capacity is 250 mAH. But 250 doesn't go into 1008 evenly?

 

[andrevdh]

The amp-hour rating of a battery is a very crude evaluation quantity of a battery. This given figure was arrived at by discharging the battery over some chosen period of time, it seems 20 hours is popular for some reason, drawing current from it at such level that the battery actually just makes it to the end of the fixed time period (which might be different for different manufacturers - they are not oblidged to keep to any specs.). The load is therefore adjusted to obtain the "right" amount of current so that it just survives the ordeal. Like how hard should an employer make his subjects work so that they only just make it to retirement? Your problem is allmost the same - you know how long and how hard (you want them to work), the question is just how many (batteries do you need for the task). This means that this value is of no real value to your problem. If you do decide to take it as a guideline then the amount of current that one such (set of) batteries can deliver for 504 hours come to about 0.5 mA, which indicates that they cannot do the task on their own, they need at least three more sets (that is quite a lot of batteries to keep one LED happy for three weeks), maybe one extra set to play it safe.
Otherwise you need to get info from the manufacturer or test their capacity yourself, maybe they perform much better at a lower current?

 

[Office_Shredder]

adc, now for the beauty of significant digits. Since it's 2mA, there's only one siginificant digit, and your actual answer is 1000 mAH

 

[andrevdh]

That is the capacity you need is

$$1000\ mAh$$

and the capacity of a (set of) batteries is:

$$250\ mAh$$

so you require:

$$1000/250 = 4$$

(sets of) batteries. But as I tried to explain the 250 mAh only tells you something about one specific situation and (maybe) nothing about the situation you are interested in.