Assuming that the capacitor is fully charged from an external source, and then connected to a dead or near dead battery, will the battery receive some charge? Assuming the battery is rechargable.

Considering that battery capacity is measured in 10's of kiloJoules for NiCd batteries, and 10's of MegaJoules for car batteries -- and a capacitor's energy is generally a fraction of a Joule (220 uF 15Volt = 25 milliJoules) -- that "charge" to the battery is fairly insignificant. Even a supercapacitor at 1F, 12V is only 72 Joules. That's not much compared to 72 kiloJoules, or 72 MegaJoules.

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yes it can
yes it can becasuse the capacitor stores the charge, which can be transmitted to the battery
A capacitor will charge a battery only if it's voltage is high enough to charge the battery. It will only charge the battery while the voltage is high enough and unless it's a hefty capacitor bank, it will not charge the battery much at all.
it might take a minute charge,but this is not really a good way to charge a battery. all batts are not the same and therein lies the devil is in the details problem. there are a few books on batt maintenance. chk these and study them, not many folks understand batts at all. electrochemical batts are different too (cars). always remember it is science not witchcraft. your cap won't have the sustained current required for a charge.
Only if its voltage is higher than the voltage of the battery, and for the amount of time that it remains that way. But I wouldn't hold out much hope of doing this on a practical level - the energy density in terms of volume of a battery is about 1000 times that of a cap. Even a 1/10th recharge would require a volume of about 100 to 1.
Yes. The problem is that the brief current flow from a charged capacitor will not add much to a dead battery. You would need a lot of capacitance and a battery with very low current capacity for this to work. The concept is OK but practicality of the scheme is not good.

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