Those two sentences can have very different meanings.
Current passes through a conductor.
Absent further context, that is likely to be taken as a general statement about the nature of current. It is what current does.
Does current get annihilated when it contacts a conductor?
--No, current passes through a conductor.
Current is passed through a conductor.
Absent further context, that is likely to be taken as a statement about a particular situation, not a generality, for example: "In this experiment, current is passed through a conductor."
current passing through a conductor uses the present participle of the intransitive verb to refer to an ongoing action.
current passed through a conductor uses the past participle of the transitive verb to refer to a completed action. That which does the passing has done it.
If you wanted to create the sense of ongoing action with the transitive verb, it would be current being passed through a conductor.
If you wanted to create the sense of completed action with the intransitive verb, it would be current having passed through a conductor.