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Well.. you well know air is an insulator.. it does not allow electricity to pass through it (under normal conditions).. these are called as di electrics.. however.. you can force them to conduct.. potential difference is basically like a kick to the electrons. higher the potential difference.. higher you are forcing the electrons to go through.. and insulators are these stubborn things that just don't allow the electrons.. so ultimately what happens?? the electrons win.. this is what we call as dielectric breakdown.. you see this in nature during storms.. yes i am talking about lightning.. So you see in order to breakdown air you require certain min. potential difference to reach or.. as you said we need that high voltage.. i believe break down voltage of air is about 10^8 volts.. (do check).. so when that happens.. electrons ionize the nitrogen molecules and excite them.. when they get dexcited they re lease blue color light which you can see..!! same is with sparks.. they are mini lightnings!
exactly what @Mashy said.. Voltage matters.. more the voltage, more strongly the electrons are kicked.. and so, even air which is an insulator at low voltages acts as conductor and lets electricity to pass through.. As electricity passes through air, you see that spark.. That is basically due to the atoms exiting and reaching a state of higher energy and then again falling back to ground state by releasing energy, which you see as spark (light).. the excitation of atoms is caused by electrons and ions colliding with them.. and yeah, the dielectric potential of air is 3*10^6 V/m
in wiki its given as 327 volts as the minimum sparkover voltage for dry air at stp..
what exactly is given?
http://en.wikipedia.org/wiki/High_voltage#Sparks_in_air see last line of the SPARKS IN AIR para
read the very 1st line of that para.. Anyways its not very clear after the first line.. and the unit isn't appropriate either.. it should be either V/m or V/cm.. You can see V/cm in 1st line.. can't really say about anything after 1st line.. The first line says if you place two spherical conductors 1 cm apart in air and apply PD of 33 KV, air will act as conductor..
The quantity responsible for the electrical breakdown (spark over) is the electric field strength i.e. volts/cm. (voltage gradient), not just voltage difference. The parameter that defines this critical value for a given substance is the Dielectric Strength which for dry air is 30KV/cm.
Oops! ujjwal just beat me.