Simply, a currant is a dried fruit used in cooking. It is either a small raisin or a red berry. On the other hand, current has a few different definitions. Often it means "happening in the present time," as in current events. The other meanings have to do with the flow of a natural element: water, air, or electricity.

Currants are small, sweet, seedless dried fruit that are similar to raisins. These fruits are often used in baking, cooking, or eaten plain as a snack. They add a tartness and sweetness to dishes and are commonly found in cakes, pastries, jams, and desserts. Here are a few samples of the correct use of currant:

I sat on the cool wooden floor outside Mama's bedroom, a bowl of black currants resting quietly in my lap. (Salt to the Sea)

His products start with fresh licorice root that he sweetens and seasons with chocolate, sea salt, coffee, passion fruit, chiles or the juices of currants, cranberries, strawberries or cherries. (The New York Times)

Current used as a noun has to do with movement: a river's current, a current of air flow or wind, and electrical current. More often, current is used as an adjective and refers to the here and now. For instance, the current situation and its current issues aren't concerned with what happened ten years ago or what's going to happen. Current clothing styles probably don't include 1940s "zoot suits" or what the aliens will be wearing in next year's summer blockbuster.  Here are sentences that illustrate the ways current is used:

The current El Niño weather pattern is increasing the chances of wetter-than-average conditions for California, Swain said. (The New York Times)

The current carried him swiftly downstream, but he was also making a little progress across the river. (A Long Walk to Water)

The sharp currents of wind could be seen in whorls of snow twisting like miniature tornadoes. (Native Son)

Let the "a" in currant remind you of a small tart raisin. And let the "e" in current remind you of present news and events.