Origins
The English word 'current' entered the language around 1290, from Old French 'corant' (running), the present participle of 'courre' (to run), which descended from Latin 'currere' (to run, to move quickly). The word is, at its core, a present participle: it means 'running' — whatever is current is running right now.
The Latin verb 'currere' is one of the great source verbs of the English vocabulary. From it descend not only 'current' but also 'occur' (run toward, happen), 'recur' (run back, happen again), 'incur' (run into), 'concur' (run together, agree), 'excursion' (a running out), 'precursor' (one who runs before), 'course' (a running, a path of running), 'discourse' (a running back and forth), 'corridor' (a running place, a passageway), 'courier' (one who runs, a messenger), and 'curriculum' (a running, a course of study). The PIE root *kers- (to run) also produced, through a different linguistic path, English 'horse' (via Germanic) — the animal that runs.
The adjective sense of 'current' (belonging to the present time) developed naturally from the participial meaning. What is current is what is running now, as opposed to what ran before (past) or will run later (future). 'Current events,' 'current affairs,' 'the current situation' — all employ this temporal sense. The word implies motion through time: the present is not static but flowing, running forward like a stream.
Latin Roots
The noun 'current' in its physical sense — a body of water or air moving in a definite direction — preserves the Latin most literally. A river current is water running. An ocean current is a great river of water running through the sea. An air current is wind, air running in a direction. The Gulf Stream, the jet stream, the trade winds — all are currents, all are named by a Latin word for running.
The electrical sense of 'current' dates to the mid-eighteenth century, when scientists began conceiving of electricity as a fluid that flows — runs — through conductors. Benjamin Franklin and his contemporaries adopted the water metaphor: electrical 'current' runs through wires as water current runs through rivers. This analogy, while imperfect (electrons do not flow like water), proved enormously productive for understanding and teaching electricity. The unit of electrical current, the ampere, measures how much charge runs past a point per second.
The noun 'currency' (money in circulation) extends the metaphor further. Money is 'current' insofar as it circulates — runs from hand to hand, flows through the economy. A currency that nobody accepts has lost its currency: it has stopped running. The double meaning of 'currency' (the money system of a country; the state of being current or widely accepted) preserves this etymology: both senses rest on the idea of running, flowing, circulating.
French Influence
'Curriculum' (originally 'a running, a race-course' in Latin) entered English as a term for a course of study — the intellectual race-course that students run through. 'Corridor' (from Italian 'corridore,' a runner, a running place) is a passageway — a space for running through. 'Courier' (from Old French, ultimately from Latin 'currere') is a person who runs — a messenger.
The PIE root *kers- connects 'current' to an unexpected relative. Through the Germanic branch of Indo-European, *kers- produced Proto-Germanic '*hursaz,' which became Old English 'hors' — the modern word 'horse.' The animal that runs and the word for running share a common prehistoric ancestor. A horse is, at its deepest etymological level, 'the runner' — and a current is 'the running.'
In modern usage, 'current' functions seamlessly across scientific, temporal, and metaphorical registers. A current of thought, a current of opinion, the current in a wire, the current in a river, the current president — all are unified by the ancient Latin image of running, of forward motion, of something in progress rather than at rest.