Voltage, Current, and Resistance are interrelated. Simply to answer your question, you can't have voltage without current, nor current without voltage based on Ohm's law. Each one must have each other in some way or another. Now I'm going to explain it
V=IR is a well known equation for EEs called Ohm's Law. This has to be true every where. So when you supply a particular voltage to a circuit, there is an associated impedance (even if it's an IC, capacitor, inductor, etc). Impedance is the complex form of resistance (little harder to describe). Everything in circuits can be represented (ultimately) by impedance. So ohm's law is really this:
V=ZR where Z=R+jX
[V] voltage
[Z] impedance
current
[R] resistance
[X] Reactance
Now as to what current is. I'll give you the classic water-pipe example. Imagine that you have a water-pipe of a certain diameter (R). water in the pipe is considered the electrons. Imagine voltage as being the water pressure (or push) in the pipe. Finally imagine current being the amount of water that flows through a given portion of the pipe. If R = infinity, this would indicate you have no pipe and thus no current can flow. It's like blocking the pipe up with something. If the pipe is infinitely big, water would flow really easy with whatever pressure you supply to the water. But if your pipe is say 1 ft in diameter. you can't just pump 600gallons/sec through it without having a very strong pump (or voltage).
I hope this description helps a little. I tried to explain the best way possible. The key is that all circuits have some form of resistance and thus must follow Ohm's Law
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Justin Coulston
TheModernEngineer.blogspot.com