Battery

e

At least in english, "capacitance" means how many Farads a capacitor has, but "capacity" also how much any container can hold, including "battery capacity". I suspect it's similar in French. (Wasn't it a bushism that French doesn't have a word for entreprenuer?)

Given the nonlinearities of real-world batteries I expect there's a constant of the order 3 or 5 or so (and that depends on chemistry) that comes into a true apples to apples comparison.

The differential equations for most batteries (replacing I =3D C dV/dt for the perfect capacitor) are highly nonlinear and at least somewhat dissipative but can be written, battery and power engineers write the equations all the time in their modeling. I know of some proprietary models but I suspect that this is an exercise done by power engineering students all over the world today.

Tim.

e

Hello Jean-Christophe,

The capacity of a battery is expressed in Ah (or mAh). A battery can produce a certain current (I) during a certain time (T) while maintaining a certain minimum output voltage. The product of I*T is called capacity.

When you discharge a battery with a larger current, it will reach its minimum required output voltage in a shorter time with respect to the I*T product when discharged with low current. So the I*T product (the battery's capacity) depends on the discharge current. Faster discharging (more current) results in less usable capacity. This is partly caused by the battery's internal resistance. Also lower temperature results in less capacity, in particular at high discharge current.

For example go to:

f This shows the discharge curves versus time for various discharge current. when assuming a termination voltage of 1 V, you can calculate the capacity (Current-Time product) for the various discharge currents. You will see a very non-linear behavior, so you cannot compare it with just a real capacitor.

For this battery, when discharging from 1.4 to 1V with 700mA/6.5 hours, you need a capacitor of C =3D delta(Q)/delta(U) =3D (0.7*6.5*3600)/0.4=3D 41kF. While the battery is almost depleted when reaching 1V, the capacitor has still a significant charge (with its associated stored energy). Here you see you cannot compare a capacitor directly with a battery.

Look under "nominal capacity" to see how GP specifies the capacity for this type of battery.

Best regards,

Wim PA3DJS

Remove the obvious 3-letter combination in case of PM.

So what is meaning of C in the case of a battery ?

Thanks Wim.

I don't compare a battery with a capacitor. Since I*T is homogenous to Ah (1 Ah = 3600 Coulombs) one can replace I*T with the Ah value of a battery.

What I can't figure out is the meaning of C for a battery, as in C = I*T/U ?

This is capacitance:

I = C * dV/dt

Nothing more.

Batteries don't satisfy the above equation very well, since their physical mechanism is chemical, unrelated to capacitance.

Tim

-- Deep Friar: a very philosophical monk. Website:

Have Fun! Rich

This is rather the expression of the current thru a capacitor due to a voltage variation, a capacitance is defined as C = Q/U

Yes I understand that.

If a fully loaded 12V 1Ah battery is not connected at all, ( no charge nor discharge current ) then is C=I*T/U valid ?

I guess it is, since I*T/U is homogeneous to a capacitor [L^-2 M^-1 T^4 I^2] - now what does mean C ?

C is a made up approximation, not a unit of measure, even though it is sometimes used that way. It expresses the capacity of a battery in Ampere Hours at some specific discharge rate. (By "made up" I mean compound in the sense of the term "kilometers per hour", but nowhere near as exact as kph.) As generally used in discussion, C is the manufacturer's rating, not something we derive from our own measurements.

Ed

Hello Jean_Christophe,

It is just as I explained and what is shown in the PDF, they just use C to denote the "current*time" product. There is no other math behind it. Forget the formula for a capacitor. letters, like C, are used in various technical domains for different phenomena.

Best regards,

Wim PA3DJS

Show me a charge-o-meter (or whatever measures Q in the real world) and I'll accept your definition as more practical. I'm not saying it's wrong, just that I don't own a charge-o-meter and can't measure charge. SPICE doesn't keep track of charge, etc., it keeps track of voltages and currents in its differential equations.

For an electrical engineer, I =3D C * dV/dt, for no other reason than that we own ammeters and voltmeters.

Electrometers aren't really truly native charge-o-meters; most (all?) of them use a known capacitor value and actually measure voltage or current as that known capacitor is charged from the unknown charge. There's probably some solid-state effects that let you measure and count actual individual electrons (I'm old enough that we did this with the Millikan Oil Drop experiment... that's a true charge-o- meter!)

I don't think there's anything awful about treating storage batteries as capacitors in some mental models, and then later considering the nonlinearities. Certainly as you charge up a storage battery, it's open circuit voltage goes up as well, so there's a useful but limited range where I =3D C * dV/dt. This will give different numerical values of C (factor of 10?) than the method you use, depending on what V is when we measure dV/dt. Do it for a nearly discharged battery (say a lead acid cell at 1% capacity) and you'll get a very different number than a 90% charged battery.

Tim.

I think there's nothing inherently wrong with treating a battery as a capacitor EXCEPT that a battery has a series resistance that varies with state of charge. I vaguely recall such a Spice model that had R=f(charge). I'll look thru my files and see if I can find it.

...Jim Thompson

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| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
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"Democrat", "Liberal" and "Leftist Weenie" are simply politically
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Ok, thanks again.

Right, I see the point. Thanks Tim.

"Jim Thompson" schreef in bericht news: snipped-for-privacy@4ax.com...

Somebody wasn't paying attention during chemistry lessons.

A battery is chemical energy store, and the output voltage is proportional to the logarithm of the concentration of the chemicals being used up (effectively the charge) - as described by the Nernst equation

In a capacitor the voltage across the capacitor is a linear function of the charge.

As Jim correctly says, the series resistance of the battery complicates the voltages you actually see - not only is there a voltage drop across the internal resistance, which make the voltage output current dependent, but the current drawn through the internal resistance generates heat, which changes the temperature inside the battery and consequently the "constant" in the Nernst equation, adding another source of voltage variation.

--
Bill Sloman, Nijmegen

Surf for "S.C.Hageman" "battery models"

Not quite what I remembered, but tabular for many types.

If you can't find it, E-mail me and I'll send you the zip.

...Jim Thompson

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| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
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| E-mail Icon at http://www.analog-innovations.com |    1962     |
             
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Like any capacitor; that means it opposes a change in voltage. But, when one tests that with an AC voltage or a changing load to be more PC, one "sees" the internal resistance as being large in comparison.

Hmmm...a capacitor "does not care" about its physical mechanism. Charge an adjustable capacitor when at maximum, and then rotate (say, in one second) to minimum and measure C and V in both cases. Now take 2 plates with area to get same capacitances and move form close to far for same change in same time and same initial charge voltage. Now take a varicap diode (or a number in parallel) to do the same exact thing. Here are three different "physical mechanisms" that you cannot argue about and they will give similar end-points (depends on losses, etc). Now take a small black box and do the same, but change the voltage and look for a change in capacitance. Open it up but take care if H2SO4 pours out... Or maybe it is a solid lithium electrolyte.. ..have fun.

Worse still, what if capacitance is a function of voltage, as ceramics or semiconductor junctions are? ;-)

Tim

-- Deep Friar: a very philos>> This is capacitance:

Hi Jean,

C is Amp hours T is Time (usually seconds) I is Amps

Originally I thought you had a peurkert effect question ;D

See

's_law

Also Have a look here... Section 7.3

T=C/I^N where N is the peukert number of the battery. T = time C = Ah I = A

Basically the higher I is the shorter the usuable T(time) will be. This is mostly used for Lead acid 'wet' batteries.

Cheers