Electricity, Arthur had studied it before.
Even though not extensively, but if it was just simply for recharging, that would be enough.
At the very least, he knew about generating static electricity through friction.
He also knew how to use a flask to melt sulfur, then insert a wooden handle to facilitate a better frictional generation of electricity.
He could also create a simple energy storage device using a glass bottle, a metal chain, and tin foil on the inside and outside.
Of course, if all these methods were still not sufficient, one could always utilize nature... no, become nature's laborer.
A kite, was enough to 'contact' lightning.
Of course, Arthur wouldn't be the one tugging at the kite.
He had...
[Invisible Hand]!
Anyway, if he wanted to recharge the [Mark of Thunder], there were plenty of ways to do so.
And doing so would thwart the little schemes of that Countess.