time dependent current equation for simple battery/resistor combo 1

[mielke]

I'm having trouble finding an applicable equation to use...
Let's say I have a simple circuit with a voltage source and a resistor. I know the initial voltage of the battery and the resistance of the resistor, I want to know the current (or voltage) with respect to time.

what equation will tell me this?
what other variable about the battery do I need to know?

I understand how to use the amp-hour rating of the battery, but I want more detailed idea of the voltage/current over time. of course both will slightly drop off and then go to zero over time, what equation describes this?
Thanks!

 

[racookpe1978]

Well, meet us part way here!

1. What is the initial current: YOU need to do that math.
1A. What will you decide is the final current - the time will you say "It has stopped"?
2. Why do think anything (other than internal battery loss/resistance due to battery chemical heating) else will change with time?
3. How accurate do you need to be?
4. most important; What is the capacity of the battery, and what is the capacity at the discharge rate that you actually start with?
5. How will your load's resistance change over time? Over temperature? or will it be constant?
6. What will the change in resistance in your wire be as a function of temperature? Why do you think that resistance (in the wire) will change with time? Do you care about that level of accuracy?

Most important is the battery capacity at various discharge rates, and at what time do you consider the discharge "stopped"?

 

[mielke]

Thanks racookpa for the quick response...
1)1.2mA (assuming 1.2V and 1kohm)
1A) I don't have a final current I'm looking for an equation that will tell me the current at any moment in time
2) just from my experience that batteries die when used
3) looking for a theoretical solution
4) do you mean mAH? if so lets say 500mAh
5/6) good question, I don't know...I was assuming that my voltage and current would proportionately drop off over time. In a simple circuit like this is resistance of a resistor dependent on the current also?

 

[Compositepro]

What you ask is completely a function of the construction of the battery and will change with the age of the battery. You haven't even stated what type of battery it is. There is no theoretical equation, but you may be able to find empirical data on your specific battery type.

 

[LiteYear]

I think perhaps, you know not what you ask!

This ought to get you started:

http://doc.utwente.nl/64556/1/BatteryRep4.pdf‎

 

[mielke]

Thanks LiteYear, I'll read over that.
I've been looking at Peukert's Law but have a feeling it didn't give me what I wanted.

Compositepro, let's say a NiCd. is there an empirical equation out there to give voltage for a continuous discharge to a resistor?

 

[IRstuff]

To what accuracy? Given that every battery behaves differently, to some degree, no equation is going to accurately predict the behavior without having some specific and accurate performance parameters.

Also, to what end? Do you care about the voltage output? If not, why not?

TTFN
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[IRstuff]

there's

http://www.che.sc.edu/faculty/white...of lithium-ion and nickel battery systems.pdf

http://scholarcommons.sc.edu/cgi/viewcontent.cgi?article=1057&context=eche_facpub

http://users.ece.gatech.edu/rincon-mora/publicat/journals/tec05_batt_modl.pdf

TTFN
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[VEBill]

Some battery data sheets have lovely curves showing the terminal voltage (and even the effective series resistance in case you want to get really precise) as a function of amp-hours consumed (or some similar measure of where you are in the capacity). In such cases, it'd be a doddle to prepare a spreadsheet to model the voltage over time.

 

[itsmoked]

NiCads sustain a pretty constant 1.2V during their useful discharge. As they reach end of charge the voltage drops off a cliff.

You can approximate the discharge time with a straight line based on the battery's published discharge rate curves.

Because what you're asking changes with battery life most products now incorporate charge monitor chips or "fuel gauges" that can track the reduction in battery capacity over the battery's useful life.

Keith Cress
kcress -

http://www.flaminsystems.com

 

[racookpe1978]

Do you see what IRStuff and itsmoked wrote about how batteries behave differently over different time periods of (1)charge and (2) battery discharge rates and (3) prior-to-use battery shelf time?

OK, same goes for loads. Sometimes. Not always. 8<)

For example, a simple resistance heater load. No real change once it is heated up.
A old-style incandescent lightbulb. Once it heats up, resistance stays proportional to battery current flowing through the bulb (less current = less heat), but as an original old-style alkaline battery discharges discharges, the bulb would keep "on" but would get gradually less and less bright. Current still flows through the incandescant bulb, but, it just isn't enough to see with.

New electronic LED bulbs stay bright - but only as long as the battery voltage is high enough to "trip" the LED "on". Battery voltage goes down (self-discharge or use or whatever) at some point the LED bulb suddenly goes "off" and doesn't shine at all.