How do you compare batteries to caps?

As capacitors become larger (capactitance-wise) they are starting to replace batteries. Is there a way to compare the useable current from a capacitor rated in Farads with a battery rated in Amp/hours? Or to put it simply, is there a way to compare the amount of energy stored in a battery with the amount of energy stored in a capacitor?

Charge stored in a capacitor is capacitance * voltage. If you apply 1 Volt on a 1-Farad capacitor, it’ll store 1 Coulomb of charge. 1 Amp is 1 Coulomb per second, so you could argue that a 1-Volt 1-Farad capacitor is comparable to a 1-Volt 1-amp-second (or 0.28 milliamp-hour) battery.

Of course things aren’t quite that simple. Voltage of a capacitor decreases linearly (i.e. proportional to remaining charge, at least for an ideal capacitor), while a battery voltage drops more slowly.

From here, the energy stored in a capacitor is CV[sup]2[/sup]/2. For a 2 farad capacitor charged to 12 volts, this would be 144 joules. Using the conversion conversion given here, that is 0.04 watt-hours. I chose 2 farads and 12 volts because I just saw a 2 farad(*) capacitor a couple days ago. It’s designed to provide a burst of energy for car stereos, and is as big as my foot.

  • Now I’m not sure. It might have been 6 farads instead of 2.

A typical AA or AAA 1.5 Volt battery is around 1000 mAmp-hour, so the energy it can produce would be 1.5 Watt-hours.

So a tiny AA battery has many times the energy storage of a very large capacitor.

OK, here’s a page with a bunch of stereo capacitors, ranging from 1 to 5 farads.

I’ll take this time to point out that while their power density is low compared to a AA battery, your AA battery probably doesn’t have a digital readout showing its voltage to a tenth of a volt, like most of these have.

Capacitors aren’t replacing batteries because capacitors are getting bigger. We’ve had big honkin capacitors around for a very very long time. Capacitors are starting to replace batteries mainly because the devices being powered are using less and less current, and the current draw for many devices has finally become low enough that a capacitor becomes a practical.

Twenty years ago, if you wanted to use a capacitor instead of a battery to back up the memory on a digital VCR, you would have needed one of ZenBeam’s foot long capacitors. These days a capacitor the size of a small watch battery does the trick. Capacitors haven’t shrunk much, but the current draw for memory chips has shrunk significantly.

>Capacitors aren’t replacing batteries because capacitors are getting bigger.

Wrongo, bucko. Capacitors are even being used to power electric cars.

Wrongo, bucko. Capacitors have been proposed to power electric cars. “Read it again Sam.” They won’t be on the market any time soon.
Safety wise there is much concern regarding the prevention of massive discharges from batteries and so too with capacitors.
I have seen capacitors as big as 55 gal. drums. A number of them were discharged via a semicurular thick sheet of copper which made a single turn wrap around a pyrex tube to create an intense magnetic field there in.
Nasty things to play with if charged at high voltage and have high capacity!

“Supercapacitors” measured in Farads, ARE reasonably recent developments, 20 yrs or so, which I know seems like forever to some dopers (the ones that play on my lawn!) but isn’t in the scheme of things.

The first thing not mentioned thus far is that batteries provide energy at reasonably constant voltage, and this is a very useful thing for many applications.

Capacitors, on the other hand, reduce the output voltage in inverse proportion to the charge supplied. (inverse square root to energy supplied) When you have removed 50% of the energy, the available voltage will be only 70% of what you started with. At 75% energy depletion, the voltage will be down to 50%.

To efficiently use all the energy stored in the cap, you need to have an application that can tolerate a widely varying supply voltage, or a fairly sophisticated regulation circuit that provides constant output for variable input, and does so efficiently (what makes it sophisticated). These have existed for about 30 yrs. but have only gotten cheap and mainstream in the last 10-15 years.

A Second problem with the supercapacitors is high internal resistance. This means that if you try to discharge them quickly (an hour would be quick) then most of the energy gets converted into heat inside the cap. So they are better for very small loads, like memory backup, where they supply microamps for several weeks.

Tell me about it. When I took Circuits I back in 1992, our prof told us that one Farad was a pretty massive amount of energy, and capacitors that big were too large to be practical in most situations. We mostly used milli- and microfarads. It’s bizarre today to think of a small capacitor capable of holding one Farad.