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I have read that we can charge a capacitor using a battery, but can the vice versa happen? My project needs to show a battery being charged through a fully charged capacitor.

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Well...only until their potentials meet in the middle. – dmckee Dec 17 '12 at 14:58
Perhaps, you need a laaaaaarger one for that :-) – Waffle's Crazy Peanut Dec 17 '12 at 15:08

Crazy Buddy's answer and related comments have made the point that you could indeed use a capacitor to charge a battery, but the amount of energy stored in capacitors is generally less than in batteries so it wouldn't charge the battery very much.

However there is a new generation of capacitors called ultracapacitors that are being developed with electric cars in mind. See for example this blog or Google to find many such articles on ultracapacitors. It seems likely that if the technology ever makes it into electric cars it will be as a combination of a battery and an ultracapacitor. Since most cars use regenerative braking, the energy generated by the braking would be stored in the ultracapacitor and would then recharge the battery. So this would be an example of using a capacitor to charge a battery.

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Let's take your question in my thought...

For instance, let us assume that we've got a capacitor of capacitance about some $100 \mu F$ and Also, a commonly used $\text{Ni-mH}$ battery of some voltage $1.5 \text V$ with charge capacities about $2000 \text{mA-h}$

Energy of the battery would be $E=1.5\times 2000\times10^{-3}\times3600$ $$=1.08\times10^4 J$$

I really bet ya that a common capacitor of some micro-farads won't charge upto that energy.

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Right, let's just say that if the capacity if 100 microfarads, the energy is $Q^2/2C$ so to get 10,800 joules, we need 1.5 coulombs or so. The voltage is $V=Q/C$ which is 10,000 volts or so again. Even if you could charge it this much, it would be pretty bad to connect it to a 1.5-volt battery. To summarize, the charging is only good if the voltage is close to 1.5 volts but capacitors have vastly variable voltage that depends on the stored energy and/or charge dramatically. Normal capacitors store much less energy than batteries because they don't change any chemistry i.e. no "burning". – Luboš Motl Dec 17 '12 at 16:31
You can buy 2 Farad audio capacitors, and I think these are usually designed for car battery voltage, and I see printed limits of 20 V. That's 800 J right there, although it will cost you $30-40. It's not cheap but it's not crazy. – Alan Rominger Dec 17 '12 at 18:23
@AlanSE: Thanks to you too Alan for adding up :-) – Waffle's Crazy Peanut Dec 18 '12 at 2:49
thank you for all your answers guys...! – Momina khan Dec 18 '12 at 15:35
How about charging a mobile battery of some 3.7 volts and 6.11 watt hour?? – Momina khan Dec 19 '12 at 11:13

A single Maxwell (for instance) BCAP0350 2.7v ultra capacitor that's about the size of a D cell has a capacity of 1300 Joules (1.3 x 10^3 J).

It is extremely useful to use ultracaps to charge batteries if the nature of the power source is intermittent and high current (say, at 35 to 175 Amps, also within spec of the one I listed).
Charge the ultracaps fast with high current and subsequently use the ultracaps to slowly charge the battery without having to worry about the battery exploding or its life being shortened by high charging rates.

Ultracaps have cycle lives in the millions, not the tens or hundreds like various battery technologies.

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All you need to charge a battery from a capacitor is to have more voltage charged on the capacitor than the voltage of the battery. The size will only affect how much time the capacitor will charge the battery. If you could charge the capacitor over and over and discharge it into the battery every time it was full it would eventually fully charge the battery.

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