Sounds like it's possible, but without more information on the specific camera battery and the UB645 battery, there's a chance things `might` go wrong. But if you're wondering if it can be done, yes it's possible, but it might take some support electronics to be able to make it happen safely for the camera.
There are two basic types of Olympus battery chargers. The first type of battery charger plugs into both the wall socket and the camera itself. There is no need to remove the battery. The other type of charger requires the square battery be removed from the Olympus camera. The charger is plugged into the wall and the contacts of the battery are connected with the contacts on the base. Once charged, replace battery in camera.
The current depends on what is connected to the battery's terminals. If nothing is connected to it, then there is no current, and the battery lasts quite a while. In general, the current is 1.5/resistance of the external circuit connected to the battery until that number gets too big, and then the voltage of the battery sags, because it can't deliver that much current.
When external source such as a battery is connected electrons get specific directions to move and condition starts
Potential chemical energy is released as electrical energy when the external circuit is connected.
The rating of "4600 mAh" is one description of the battery's capacity. It doesn't tell you anything about the delivery or discharge rate of the battery. Those depend on the external circuit that you have connected to the battery. For example, if nothing is connected to the battery's terminaks, then the battery is giving zero amperes.
HQRP Battery Charger for Olympus Evolt E510 is available on amazon.
The voltmeter would read 12 volts. An ammeter connected to to battery would only read 4 amps (12 volts divided by 3 ohms =4)
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Depending on the type of Olympus camera you own, the battery packs look different. the Olympus LI-12B rechargeable Lithium-Ion Battery for C Series Digital cameras is a small silver-colored pack that looks like a square with 4 battery windows at the top. http://www.amazon.com/Olympus-Rechargeable-Lithium-Ion-Battery-Digital/dp/B00007I409
Olympus camera batteries last on average the same as other battery brands. To extend the charge life of your camera battery be sure to not use the LCD panel since it drains the battery.
Olympus battery charges can be purchased from a number of different retailers including directly from Olympus. Other suppliers are local photography stores and eBay. Amazon also stock a wide variety of Olympus chargers. Make sure you know the model number you require as often, they are not interchangeable.
Only if you have a battery charger connected to that 110 volt AC outlet. If you are thinking about connecting live AC current directly to the battery post forget it. That would more than likely cause the battery to explode.