How fast does an electron travel in a circuit? How is it possible to calculate the speed of an electron in a circuit? What factors does it depend on?
 A: Individual electrons may have a range of speeds in a circuit (thermal motion, scattering, absorption, photon etc..) 
However the current (or drift velocity) gives the average speed of the whole electron cloud (not a single electron). 
Note again single electrons may have a range of speeds (from slow to very fast, near $c$). It is the electron cloud that makes the current and this has another velocity.
A: The speed of an individual electron cannot be c:
an electron is a massive particle and can therefore never achieve the speed of light
Furthermore, an individual electron moves very slowly in a current (mm/h scale).
The question i think you're trying to ask is how fast do electric signals travel through a wire. (e.g. if I had two lightyears of copper wire and closed the circuit, how long would it take to detect the current halfway from the source) to which i don't know the answer.
Though, I once heard the question interestingly put as: how many bits are in one meter of a gigabyte cable.
A: Electrons indeed move extremely slow.However it is not the really the electrons' motion for which the light goes on in a bulb as you switch it.Just as you find water coming out of a pipe as you open the tap (the water flows;the water at the mouth of the pipe comes out as you open the tap.Similarly the electrons push other electrons and so on and this influence propagates at the speed of light .
