pattern of moving electrons in wire under AC when we use a DC battery into a circuit the flow of electrons in wire creates a clear picture as they flow from negative terminal to positive terminal. under AC(Alternating current) we know how energy flows and what does it mean by $I_{rms}$ or average current etc. But what about the pattern in which electrons move?
 A: The detailed movement of electrons in AC current gets very complex and depends on the exact conductor being used but, simplistically, the electrons simply move back and forth (away from and then towards the generator) over a short space 
If you think of DC as a push system analogs to a straight flow of water in a hose, then AC is a push-pull system which would be like water in a hose connected to a piston that, as the piston cycles, first pushes the water down the hose and then sucks it back. 
In a DC water hose, a molecule of water can only perform work e.g. moving a turbine, when it travels from one end of the hose to the other. However, in an AC water hose, a molecule of water just oscillates around its starting location and it is just the force of the molecule hitting the next molecule in the chain that transmits the energy. The last molecule in the chain is always the one that strikes the turbine and performs the work. 
That is why AC can transmit energy over long distances. In DC, the generator must push an electron all the way down the wire to the load (and eventually back down the other side of the circuit) to perform any work. AC by contrast is just transmitting the electro repulsive force that drive electrons away from each other. (Just like a Newton's cradle transmits momentum instead of moving the spheres.)
A: Electrical current is the movement of charges, not electrons: I = dQ/dT. As far as the movement of electrons is concerned, that's called electron drift, and it is indeed as molasses.
A: "The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean (average) of the squares of the original values"
Irms refers to the root mean square value of the current over time.  This value is A/sqrt(2) if I(t) has the form A*sin(wt).  Intuitively, if you look at a sin wave from 0 to pi, the amplitude seems to be average a little more than halfway from y = 0 to y = A.
To come to this result, you would sqare Asin(wt), take the average, and then take the square root, which would leave you with A/sqrt(2).
Current is always generated by very small, (approximately) continuous voltage drops in the wire.  Think about tilting a rainstick one way or another.  So when you are using AC, you are tilting the rainstick back and forth periodically, and electrons will get pushed back and forth in an (approximately) harmonic way.
Electrons will only move a short distance back and forth in the wire because of a drift velocity http://en.wikipedia.org/wiki/Drift_velocity which is very slow to the frequency of the AC current (says .00028 m/s in the wikipedia article, this depends on the wire and current you are using and is approximate)
Hope it helps
