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Electronics/Battery behavior

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Question
I've been trying to figure out everything about batteries forever.  First comes testing them to see how much life is left in battery, like a AA, AAA, or coin cell.  All the battery testers that are sold (as well as multi-meters) only test the voltage, but isn't that not the relevant variable in determining how much juice is left?  My understanding is that volts are just the speed in which the electricity travels, whereas amps are the actual amount of electricity contained. So how does testing for voltage tell how much power is left in a battery?  Feel free to answer "it just does" if that's the case. I don't expect you to explain every concept, I just want to know how I can tell how much life my regular, non rechargeable batteries have left.

Other quick battery questions:
1)What's wrong with mixing partially used batteries with new ones?  
2)I have a wireless doorbell, and the button part required a A23 battery (looks like half AA, but 12v).  I didn't have one, so I tried connecting the positive and negative terminals from a 9v and voila, it worked fine. Why did it need the 12v?  Shouldn't something like that be able to run for years of a coin cell?

If you have any recommended reading on batteries something that explains basic electricity in an interesting way, feel free to recommend something.

Thanks so much!

Answer
A battery has an internal equivalent resistance.  This can be measured by recording the open circuit voltage.  The place a load across the resistor that drops the voltage enough to measure accurately. You can now compute the internal resistance by using ohms law.  Do you understand ohms law calculations?  If you know the voltage of the battery and the drop of voltage when you loaded the battery then you can calculate the current.  Then using the current you can calculate the internal resistance.   And so on.

http://www.youtube.com/watch?v=q58E8DdNgDs

A little more theoretical:

http://batteryuniversity.com/learn/article/how_to_measure_internal_resistance

Knowing the internal resistance at various power levels can be used to know what the battery voltage will be under circuit current conditions.

The DoorBell: Most electronic circuits will operate over a range of power/voltage.  They are designed that way in order to continue working for as long as possible even after the battery voltage is starting to die.  Perhaps the manufacturer used 12v in order to be able to assure the customer a particular advertised long life of operation using the discharge slope of the battery as it dies out down to the 9v or even lower.

Going back to the beginning you can compute the current requirements of a circuit.  Or, often you can merely measure the current drain with a cheap little VOM from Walmart for $9.97.  Knowing the circuit current drain helps to guesstimate the length of time it will supply the circuit.  Watches, for example use current in the micro or pico amps allowing them to run for days, months or even years from simple little button batteries.  It's all an ohms law matter of understanding.

I suggest you run through the first few chapters of this training = which is one of the best I know:

http://utwired.engr.utexas.edu/rgd1/lesson09.cfm

Going through the first few chapters will make you into an electrical genius and miracle worker!

ZZ  

Electronics

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ZZ

Expertise

Electronics questions about AC, DC and digital theory.

Experience

Graduate electrical engineer with over 40 years in electronic design, manufacturing, project organization and patent review. Experience in fields of industrial and consumer electronics (audio, video, acoustics, etc.)

Organizations
IEEE (Institute of Electrical and Electronics Engineers); Senior Life member AES (Audio Engineering Society), Fellow Life member

Education/Credentials
BSEE University of North Dakota

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