How do I charge this power source?

Hint 1 of 4:

Someone in the game is doing experiments with electricity.

Hint 2 of 4:

Ben Franklin is.  To find out how to help him along, see the questions in
the "Ben Franklin" section later in this file.

Hint 3 of 4:

Then you need to make sure that the battery gets power from the lightning.

Hint 4 of 4:

There's a pocket in the coat.