Why potenial drops across a resistor in an electric circuit? Why potential drop across a resistor in circuit? I want to know what causes this drop at the atomic level.
 A: I limit my answer to materials other than semiconductors here. 
At the atomic level, the electrons that are carrying charge will flow through a solid if there are lots of mobile (unbound) electrons in that material. If the conductivity of that material is perfect, it will require no work for the electrons to traverse that material. However, in the real world and at room temperature, there are things that will get in the way of the electron flow, and for an electron to make its way through such a "real world" material then requires that some amount of work be expended in the process.
Things that "get in the way" of electron flow through a material (say, a metal) are defects in the crystalline structure of the metal which, when struck by a moving electron, cause it to bounce off and seek another path past it. These defects are called "scattering centers" and the more of them you have in a chunk of material, the more work you must expend to push an electron through it. 
Where does this work come from? Well, if that chunk of material is connected to a battery so that electrical current from the battery is flowing through the material, then we know that every electron that enters the chunk of material has to exit it (current is conserved) so the material cannot "consume" electrons in order to do the work. But the voltage across the chunk of material is a measure of how hard the electrons are being pushed through it by the battery (higher voltage means harder push) and so it is the voltage that furnishes the effort which is diminished as the electrons traverse the material. Then the net amount of work required to push those electrons through the chunk is equal to (effort) x (flow) or (voltage) x (current). 
This means that if we measure the voltage above the return line potential to the battery at a series of tiny slices through the material along its length, we will see that to traverse each tiny slice requires a little bit of work equal to (the voltage difference appearing across that little slice) times (the current flowing through it).
In this way, the voltage across the chunk of material is progressively diminished as the electrons being pushed by that voltage make their way through it.
