Why Does Current Flow Through Wires With Zero Voltage Drop (Ideal Wire Question)?

Hi guys !there's something really confusing me so much and I hope to help me.what we know about current, that if there's no voltage difference then the current is zero !so what I'm not understanding how actually there's current in the wires? isn't the voltage on wire itself =0?(wire isn't a resistor) so it musn't carry any current .. must it?! I mean lets assume I have source voltage with two wires connected parallel between resistor and source voltage, so if wires don't carry any current because the voltage on them is zero, how actually there's a current through them going forward the resistor? I know there's a difference voltage on the resistor, but wires itself there's no voltage difference so it mustn't be current passing from them because there's no voltage difference on the wire "itself" , as a result how actually they are passing current at all?!

thanks

Ryan,Wires do have a little resistance. 24 AWG copper wire is about 0.25mm in diameter and has a resistance of roughly 0.1 ohms per metre.So a few centimetres of wire in a circuit will have a very tiny resistance. It's just that, in most cases, it's small enough not to affect anything and so it's approximated to zero in most calculations.It becomes important when you're using long cable runs, or when you are pushing a lot of current through the wire. This can lead to the wire heating up, and the voltage at the far end of the wire being less than you would expect if it were truly resistance-free.

MY problem is :lets assume I have a wire ye?! and I connected from one side to source voltage and from the other side to resistor ! how actually there would be a current through the resistor? I mean if the wire itself have no voltage difference, so it shouldn't carry current to the resistor at all? once again I mean like this: I believe that resistor must have a current through it, but for being a current passing through resistor we are actually using "wire" but wire itself have no voltage difference so it shouldn't pass current through it to the resistor.. but this is wrong and I don't know why!

As Sean wrote, wires do have a little resistance, so current-carrying wires do have a little voltage drop from end to end, which you can measure with a millivoltmeter. Remember that "approximately zero" and "negligible for our purpose" are NOT the same as "exactly zero". To learn about truly zero-resistance wires, look up superconductors and superconducting coils.

So voltage is electric potential -- if you have something with more positive ions on one end and more negative ions on the other end and you link them with a conductor like a copper wire, electrons will jump from the source of negative ions into the wire -- these will push other electrons out of the way (further down the wire) -- in turn those electrons will push other electrons, and so on until electrons pop out of the wire at the other end into the "container" of positive ions.This is a bit like a long line of dominoes standing up -- when you push one over at one end there's a ripple effect.So voltage is the difference in electric potential (the "pressure") "pushing" the electrons -- resistance is what fights to prevent the electrons from moving -- and current is the number of electrons passing a given point at a particular time (ish). I saw a great diagram about thsi on Pinterest:

One way I think it's helpful to visualize all of this is as a plastic coke bottle containing water as illustrated below:

The "height" of the water is equivalent to the voltage -- the diameter of the hole that restricts the flow of water is equivalent to the resistance -- and the amount of water spurting out of the hole each second is the current.If we increase the "voltage" -- like filling the bottle above to the 18V mark -- then there will be more "pressure" causing more water to spurt out of the hole.If we increase the "resistance" -- like shrinking the diameter of the hole -- then we will restrict the amount of water that will pass.As the others have said, even the best copper wires have a small amount of resistance. Using V = IR we also know that I = V/R. If we had a perfect conductor that had zero resistance and we connected it across a voltage source like a perfect battery, then the result would be I = V/0 and anything divided by 0 is infinity (this would be a bit like chopping the bottom off our bottle -- all the water would flow out at once). In the real world, the copper ware as a small amount of resistance, and a battery has its own internal resistance, but if you short out the two ends of a batter with a piece of copper wire (DO NOT DO THIS!!!) you would see a very high current for a very short period of time and then things would get exciting.Does any of this help?

Ryan - your mistake is in your statement in your initial question... "wire isn't a resistor".  Sorry, but it is.This is where you are going wrong.  For our purposes, everything has resistance.  As Sean pointed out above, 24AWG wire has a resistance of 0.1 ohms per metre.  So lets set up a 10V source, a 1KOhm resistor and connect them with 2 bits of 24AWG wire each 4 inches long, that's about 0.1 of a metre.  So the resistance of our wires will be 0.1 (ohms per metre) x 0.1 (metres) = - 0.01 Ohms each, 2 wires will be 0.02 ohms.  So our battery is seeing 1000.02 ohms. at 10V the current will be 10/1000.02 = 9.98 milliamps.  Each bit of wire will have 9.98 x 0.01 = 99.8 microvolts.  You probably wouldn't be able to measure this with a standard multimeter (not to any degree of accuracy anyway) So as various commenters have pointed out, we can disregard the wires in any calculations that don't have to be super-accurate.  Here's a diagram:
Now let's take this to the extreme, we'll use 1Km of each wire to connect our resistor.  So each wire will now be 0.1 x 1000 = 100 Ohms.  The picture is now very different. Total resistance is 1200 Ohms so the current will be 10V / 1200 Ohms = 8.33 mA only:
You'd easily measure these voltages on your multimeter (if you had 1KM long test leads!). So don't be fooled - all wire has resistance - it's just normally so low that we can leave it out of our calculations.  As Peter pointed out, you only get zero resistance when you use superconductors - which are normal wires cooled to almost absolute zero temperature.  Not something you are likely to encounter very often!