What will happen to the world economy if the price of oil/Coal/natural gas/electricity and all energy sources drops to lowest? Imagine if some country identifies a large resource of oil/coal/natural gas or other sources of energy that can be supplied to the entire world for the cheapest rate ever.(say for electricity 1 Cent/unit,petrol 1 cent/litre).How will it affect the world economy ?
There would be a short-term boost to profits, as a significant cost driver has dropped. There will be some substitution, as energy replaces other factor inputs (probably human labour in particular). In theory, overall, everyone collectively is better off, but redistribution effects will be significant and unpredictable.

There would be a massive shift in the geopolitics of energy: countries that are currently powerful primarily due to their energy supplies (e.g. Saudi Arabia) could become insignificant on the international scene.

If it's a fossil fuel, then there would be a catastrophic medium and long-term reduction in total global wealth owing to accelerated anthropogenic climate change. A significant chunk of global economic activity would have to be diverted to adaptation to a rapidly changing, highly random, highly variable, highly unpredictable climatic period. International refugee migrations would be of the order of a billion people or more. There would be a non-trivial probability that human civilisation would essentially cease to exist in any recognisable form.

If it's not a fossil fuel then, well, we're close to that point now: PV is around 2 (\$/€)cent/kWh for a big proportion of the world, and is expected to halve again over the next decade or so. So all being well, we'll live to see this. Note that the benefits will not be confined to one country, though: the resource is globally distributed.