Short circuit doubt Short circuits occur when a live wire comes in contact with a neutral wire due to poor insulation and stuff, and the main gist of this word short circuit is the fact that the wire gets heated up so fast it might burn. So if im getting this right then that would only mean that a very high current flows through the wire (because of joule's equation?) but my question is how? When a live and a neutral wire comes in contact then how is there a potential difference to begin with (aren't they at the same potential now?), how can current flow without voltage?
 A: In the case of AC current, the concept of difference of potential is not quite appropriate for that extreme cases. If we could measure 2 nearby points of the (short circuited) circuit, including along the windings inside the transformer next to your home, a voltmeter would show zero, if the resistance between points is negligible. Nevertheless there is an emf resulting from the variation of the magnetic flux in the transformer.
Even with zero ohmic resistance, the AC current is limited due to the transformer reactance.
But real wires have always some resistance and the maximum current can be huge enough to heat until break very quickly the weakest part of the circuit
A: There is a potential difference between the wires before they’re shorted. But once they’re shorted all that potential difference occurs all along the conductors to and from the short, as well as across the internal impedance  that exists in all real voltage sources.
Ultimately, for a properly protected circuit, the short circuit will be interrupted by an overcurrent protection device. In the case of a casual contact short     the fault may clear itself by fusing open at the location of the short.
Hope this helps.
A: Ohm's law $E=IR$. If $R$ is zero $E$ is zero, so $I$ could be anything. So, this model fails, and you must account for the fact that zero $E$ and zero $R$ are idealizations, not possible in practice.
A: 
aren't they at the same potential now?

At the point of contact, Yes. But further away from the point of contact? No.
Every wire* actually is a low value resistor. There is distributed resistance along all of the wires in your house and, along all of the wires of the electricity distribution system all the way back to the generating stations. The 14 gauge, solid copper wire used in a lot of household wiring, for example, has about 8.3 Ohms of resistance for every 1000 meters.
If the whole electrical grid was just your home and a generating station many kilometers away, then when you shorted out the wires in your home, the generating station would see a resistance of several tens of Ohms. You would see a potential difference of 0V at the location of the short, but the generating station still would see a substantial potential difference between the wires at its end.
In practice, there are other things that limit the current when you short out your home wiring. The biggest limit, I think, would be imposed by the transformer that feeds your home and probably a few of your neighbor's homes. I don't know enough of the math to describe what actually happens in the transformer, but I'm pretty sure it will not allow more than a few hundred to a few thousand amperes to flow in the circuit during the brief interval of time before the fuse blows or the breaker trips in your home's distribution panel.
Your neighbor's lights might flicker for half a cycle of the AC waveform before your breaker pops. Hopefully the power supplies in their computers and TV sets will be sufficiently robust that the the momentary disturbance does not affect them.

* Except for superconducting wires, but I'm guessing that you don't have any superconducting wires in the walls of your home.
