Question

How does AC current actually travel in wire?Explain with the help of a sinusoidal graph.

Answer 1

Well, no air molecule makes it from a talker's mouth to your ear during propagation of sound, otherwise you would complain "Good Lord that guy has bad breath!". 

Sound is transmitted by a back and fourth motion of molecules as pressure waves travel through the air, carrying information and energy, but not matter. 

Think of AC electricity transmission as an electrical longitudinal wave (experts in the field of signal transmission, such as my dad, may disagree with me). No electrons ever make it from the power plant to your house, but the information and energy carried by the AC voltage takes less than one second to travel great distances on Earth. 

Alternating current is similar, in that a wave of "electrical pressure", i.e. voltage, travels and creates an electric field disturbance which causes the oscillating electrical motion of electrons. 

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Believe it or not, electrical motion of electrons in both AC and DC is a rather insignificant portion of their motion. In fact, their random thermal motions are much more significant. 

In DC, electrons are like a colony of ants traveling along a wooden twig, traveling individually in haphazard paths, but as a net result they end up traveling in the common direction.