'Current' is Latin for 'running now' — one word uniting flowing water, electricity, and the present.
Belonging to the present time; happening or being used now. As a noun: a body of water or air moving in a definite direction; a flow of electrical charge.
From Old French 'corant' (running, flowing), the present participle of 'courre' (to run), from Latin 'currere' (to run, to move swiftly, to flow). The PIE root is *kers- (to run), which also produced Latin 'cursus' (a running, a course), 'cursor' (a runner), 'curriculum' (a running-track — the course of study), 'courier,' 'course,' 'concourse,' 'discourse,' 'excursion,' 'incursion,' 'precursor,' and 'recur.' The same root yielded Old Norse 'hross' (horse) and possibly Greek 'hippodromos' (a horse-running track). The literal sense of 'running'
The word 'currency' is literally 'running-ness' — from Latin 'currere' via the notion of money in circulation, money that runs from hand to hand. A currency that loses its 'currency' (acceptability) stops running — it ceases to circulate. The double meaning of 'currency' (money and currentness) preserves this origin: money is current insofar as it keeps running through the economy.