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 Post subject: Capacitors in series
PostPosted: Jan Tue 30, 2018 9:32 pm 
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As well all know, placing capacitors in series, the value of each cap is the same as resistors in parallel. But as I understand it, rechargable batteries don't do the same - as in their amp-hour (or miliamp-hour) rating remains the same. Why is that?

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 Post subject: Re: Capacitors in series
PostPosted: Jan Tue 30, 2018 10:08 pm 
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In series voltage doubles from batteries but current available remains the same.

Resistors are similar. Resistance doubles but current handling remains the same.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Tue 30, 2018 10:09 pm 
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Your logic is that "coulombs is coulombs", right?

So: Capacitance is coulombs per volt, whereas milliamp-hours can in fact be expressed as coulombs.

I find it easiest to deal in energy. A capacitor (or melange of same) stores energy in accord with E = ( C * V^2 ) / 2. The useful energy in a battery is the Amp-Hours times the average voltage during the discharge time.
It is difficult to relate them directly since they have different discharge characteristics.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Tue 30, 2018 10:11 pm 
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Some Bogen amps use capacitors in series because of the high B+.

The capacitance is halved (essentially, the plate separation is doubled), but the working voltage is therefore also doubled.


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 Post subject: Re: Capacitors in series
PostPosted: Jan Tue 30, 2018 10:53 pm 
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Sol wrote:
The capacitance is halved (essentially, the plate separation is doubled), but the working voltage is therefore also doubled.


Yes. And my question is why do they not act the same as a battery? To put this differently, if I have a 100 Ah battery and a 200 Ah battery, both fully charged to 12 volts, the 200 Ah battery has twice as much charge, or twice as many electrons. Basically the same way that a fully charged 200 µF cap vs a 100 µF cap, again, assuming the same voltage.

If we take two 200 µF caps, and place them in series, I now only have a 100 µF of capacitance. But if I take the two 200 Ah batteries, I now have a 400 Ah setup. Yet the voltage act the same way with a battery or a cap.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Tue 30, 2018 11:20 pm 
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Hmm.. Good question, which demands a coherent answer. I'll do my best... :P

If you look at the formula for capacitance, it depends on plate area and insulator thickness (and dielectric constant, but we can ignore that for this discussion). As Pixellany alluded to, a capacitor stores charge. The more plate area, the more charge it can hold, and the thicker the insulator, the less charge it accumulates for a given voltage, because of the increased separation of the plates. So, when you put two capacitors in series, the two plates connected together are essentially shorted, so you can consider the two insulators put together, essentially doubling the thickness, thus halving the capacitance for a given voltage.

A battery, on the other hand, is powered by a chemical reaction. Put those together and they just add, like two generators. Batteries are sources, capacitors are not. Capacitors just store charge, thus when you put them together they essentially split whatever source they are storing, as capacitors do.

Batteries and capacitors operate on completely different principles, therefore the completely different operation.

At least, that's how I understand it. :oops:


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 Post subject: Re: Capacitors in series
PostPosted: Jan Tue 30, 2018 11:31 pm 
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TPAairman wrote:
Sol wrote:
The capacitance is halved (essentially, the plate separation is doubled), but the working voltage is therefore also doubled.


Yes. And my question is why do they not act the same as a battery? To put this differently, if I have a 100 Ah battery and a 200 Ah battery, both fully charged to 12 volts, the 200 Ah battery has twice as much charge, or twice as many electrons. Basically the same way that a fully charged 200 µF cap vs a 100 µF cap, again, assuming the same voltage.

If we take two 200 µF caps, and place them in series, I now only have a 100 µF of capacitance. But if I take the two 200 Ah batteries, I now have a 400 Ah setup. Yet the voltage act the same way with a battery or a cap.


I'm not quite sure I understand your confusion here. If you have two batteries and put them in series the voltage of the system will double, similar to if you put two capacitors in series, the voltage rating of the system will double.

Conversely, if you put two batteries in parallel, the capacity (Ah) of the system will double, similar to if you put two capacitors in parallel the capacity (uF) of the arrangement will be double what each part is.

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Last edited by Hcompton79 on Jan Wed 31, 2018 12:52 am, edited 1 time in total.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 12:02 am 
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Hcompton79 wrote:
Conversely, if you put two batteries in series, the capacity (Ah) of the system will double, similar to if you put two capacitors in parallel the capacity (uF) of the arrangement will be double what each part is.


When you add the cells in series only the voltage is added. The current capacity (mAh) remains the same.

When you connect them in parallel only the capacity increases while the voltage remains constant.

Dave


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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 12:13 am 
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easyrider8 wrote:
Hcompton79 wrote:
Conversely, if you put two batteries in series, the capacity (Ah) of the system will double, similar to if you put two capacitors in parallel the capacity (uF) of the arrangement will be double what each part is.


When you add the cells in series only the voltage is added. The current capacity (mAh) remains the same.


Which means I stated it wrong earlier, but the actual question is still there - if I connect two batteries in series, the ciurrent capacity remains the same. If I connect two capacitors in series, it decreases.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 12:31 am 
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As I suggested earlier, use stored energy and it will all make sense.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 1:09 am 
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I apologize, I did make a mistake in my earlier statement which no doubt added to the confusion. I have corrected my previous statement to say that two cells in parallel have double the capacity as it should have said originally.

As to the question as to why capacitors lose capacity as they are they are connected in parallel, it has to do with the ratio of charge (Q) to volts (V) which are the two primary characteristics of a capacitor.

Lets say that you have two capacitors that are charged to the same voltage (V) and have the same plate area meaning they carry roughly the same charge (Q). If we take these capacitors and put them in series we are connecting a plate from each capacitor together this equalizes the charge (Q) on these two plates effectively resulting in zero (Q) for these two plates. Now, this also has the effect of increasing the voltage rating, and any induced voltage (2V) between the plates because we have in fact created a capacitor with the same effect as one with twice the plate spacing. Since capacitance is the ratio of Q to V and we have the same charge but twice the voltage the ratio is 1/2 of what is was for each individual capacitor.

Attachment:
capacitor.png
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Last edited by Hcompton79 on Jan Wed 31, 2018 4:49 am, edited 1 time in total.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 1:35 am 
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I missed a biggie: For the MAH capacity of batteries to add, they have to be in parallel!!----D'OH!!

Otherwise, current will flow only until the weaker of the two goes flat

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 4:19 am 
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Voltage, resistance and current are not the same thing and can't be randomly interchanged with each other..

Power is a constant.

Two equal batteries in series doubles the energy. Two equally charged capacitors in series doubles the stored energy.

Same as if you put them in parallel.

You can't equate mA directly to resistance by mixing apples and oranges.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 5:42 am 
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Greetings to Michael and the Forum:

Michael writes:

Quote:
Which means I stated it wrong earlier, but the actual question is still there - if I connect two batteries in series, the ciurrent capacity remains the same. If I connect two capacitors in series, it decreases.


Does it? Yeah, I know, answering a question with a question and no, I'm not from Maine. :D

Capacitors do not pass DC, so we are comparing apples to oranges. If we are talking AC, current through a capacitor is proportional to reactance. Capacitive reactance is given by the formula 1/(2 Pi FC) where C is the capacitance in farads and F is the frequency in Hz. If you apply an AC voltage across a capacitor, the current will be given by the reactance version of Ohm's law: I=E/Xc. If you halve the capacitance by placing two capacitors in series, double the frequency of the applied AC and you will have the same current as before.

The maximum permissible AC current through a capacitor is limited only by it's internal losses. It is possible to blow one up through exceeding its limitations, but ,other than that, the AC current through a capacitor is determined by external factors as well as its capacitance. For DC current, there isn't any.

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 4:10 pm 
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Maybe just slightly off-topic, but still relevant:
The definition of "DC" in common usage is sometime ambiguous. Rigorously, DC means that the value is not changing, but does this mean forever? No....you can operate a DC radio for an hour an then switch if off. While it is ON, the input current is DC.

So, try a revised definition: "DC" means that the value is not changing over the period of interest. Better yet: The rate of change is slow enough that we can treat it as unchanging for convenience in the analysis.

Now we can more easily compare capacitors to batteries: both have the ability to store energy and release it in a controlled fashion. The major differences include the shape of the discharge curve, and the ability to reverse the process. ( recharging )

As discussed earlier, working in energy units can help the analysis. What does NOT work is to try and apply the rules of capacitors to batteries. The fundamental reason is that a battery does not have the simple formula for charge and discharge as does a capacitor.

One fundamental difference with respect to series and parallel arrangements:
1. Both batteries and capacitors behave the same in parallel: the voltage is the same, and the ability to deliver current is additive. With batteries, however, the voltages must be matched. Capacitors must be similar only in terms of voltage rating.

2. In a series arrangement, however, there is a big difference. Batteries with different discharge curves don't follow simple rules when placed in series. Crudely, they will support a load with some predictability only until the smallest one goes dead. Capacitors, OTOH, follow very simple rules.

On-topic bottom line. You can't apply capacitor rules to batteries, nor can you do the obverse.

Off-topic bottom line. A voltage or current is DC if it changes slowly enough to allow the use of "DC rules"

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 Post subject: Re: Capacitors in series
PostPosted: Jan Wed 31, 2018 5:43 pm 
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Quote:
f we take two 200 µF caps, and place them in series, I now only have a 100 µF of capacitance. But if I take the two 200 Ah batteries, I now have a 400 Ah setup. Yet the voltage act the same way with a battery or a cap.


Apples vs. oranges. The capacitance of a capacitor is a physical effect determined by the dimensions of the plates or conductive surfaces, the distance between them, and the material between them. It does not tell you how much charge or energy is present. Kind of like the size of an air tank in gallons does not tell you how much pressure may be in it.

The diagram given above of two capacitors in series is slightly incorrect. The fields on the inside plates do not cancel. The inside plates are connected together, so they have to be at the same potential. Consequently, the applied charge is divided between the two plates. Spreading electric charge over a greater area reduces the electrostatic potential and with it the capacitance. In other words, if you take two identical capacitors and put them in series, the capacitance is halved because one unit of "charge" is divided between the two inside plates.

The term ampere-hours tells you how much charge a battery can deliver in a given amount of time regardless of terminal voltage. Numerically, one ampere-hour is 3,600 coulombs. The ampere-hour rating of a cell depends on a variety of factors such as physical size and construction, the particular chemistry used, temperature, age, etc. These physical and chemical characteristics do not change when cells are connected in series; the A/Hr rating is fixed by design and cannot (safely) exceed what the weakest cell in the string can handle.

Power is equal to volts times amps, so if two like cells are connected in series, the voltage is doubled and so is the available power. Likewise, two like cells in parallel would double the available current and along with it the available power. However, parallel connection of battery cells is unpopular because batteries that start out identical seldom stay that way for long. Heavy currents can flow back and forth between the stronger and weaker batteries and they wear themselves out sooner. (If one of the batteries shorts out the fault current can become excessive). It is more satisfactory to use one battery that has adequate capacity for an application than it is to connect multiple batteries in parallel.

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