We know that if Single Line to Fault occurs, then fault current flows to the earth. I want to know whether the current will return to the source or not. For the current to flow we need a closed path.
How it is possible for current to flow in a open circuit if you say that current does not return to the source.
The word "Earth" is sometimes misleading. I think (if I get the sense of your question right), it is more properly called a "Protective Earth". In home electricity supplies, one side of the supply is "tethered" to the same potential as a protective earth circuit. This latter is simply a system of conductors, going through the third "Earth" pin on the socket outlet, that tethers any conducting surface of an electrical appliance to the one (called the "Neutral") side of the supply. The other side of the supply is called the "active".
If a fault happens in an appliance such that the active touches the conductive housing of an appliance (say of a toaster), we have a dangerous situation, since anyone touching the appliance can then get an electric shock. However, if the housing is connected to the protective earth circuit, there is a redundant path back to the supply's neutral. This leads to a high current in the redundant path and hopefully a blown fuse in the supply live.
A more modern and safer way to achieve this protection is earth leakage protection - a system that detects, through the Ampère-law-begotten "magneto motive force MMF)", when the current through the active is different from that through the neutral. In this system, both active and neutral lines pass through a torus-shapen ferromanetic core. If the current in one doesn't match that in the other (i.e. the current going into the appliance through the active is not the same magnitude but exactly out of phase with the current coming out through the neutral), then there is a nonzero $\oint \vec{H}\cdot{\rm d}\vec{\ell}$ ("magneto-motive force") around the core and thus an AC magnetic field though a sense coil wound threading the torus- by Faraday's law, this begets an EMF in the sense coil which trips a circuit breaker. These devices can be made very cheaply and are extremely effective - shutting off within milliseconds if an imbalance of more than typically $50{\rm \mu A}$ is sensed.
Lastly, electric current can in general flow without a return path through the mechanisms of displacement current and capacitance. See my answer to the question "Does alternating current (AC) require a complete circuit?" for details.
Lastly, there have been some really bizarre truly one-line power transmission systems thought of in the past, where the one line works as a waveguide and does not need a return path. See the Wiki Page for the Goubau Line for details.
For the current to flow we need a closed path.
This is wrong. For current to flow, we need potential difference (closed path thing is an Engineering setup to maintain potential difference with Battery or Generator).
In electronic circuit theory, a "ground" is usually idealized as an infinite source or sink for charge, which can absorb an unlimited amount of current without changing its potential. Earth's potential is close to zero which remains unaffected by addition of charges. So, there's always a potential difference maintained with source even when direction of AC changes. Half of times, source is at higher potential than Earth and half of times, it's at lower potential. But, it's never at equal potential to Earth.
So, Earth doesn't setup any type of circuit with source. It merely maintains a potential difference which is the only thing necessary for current flow.
Actually the current which flows to the earth is distributed all around the earth like what happens on charging a conductive sphere all the charge is uniformly distributed over it. And yes some the charge returns to the source but it is of negligible amount and it does not enter the circuit it just reaches the source hope it cleared your doubt
First of all a fault in line/appliance does not always implies that current will flow to earth, during some faults, the parts of appliance get join and due to change in resitance and therefore change in current intake set off fuses and circuit breakers.
protective earth (PE), known as an equipment grounding conductor in the US National Electrical Code, avoids this hazard by keeping the exposed conductive surfaces of a device at earth potential.
The question arises what happens if somehow this ground line gets connected to a hot wire.
Simply a current flows from the hot wire to ground, and as it draws a large current again a fuse may break to indicate a fault in apparatus.
No the charge that flows from the appliance/source that goes as current during a fault does not return to the source.
Your understanding of flow of current only in closed circuit seems to be based on simple electrical circuits in which a battery or source facilitate the flow of current.
The basic definition of current is the flow of charge from high potential to low potential, it does not take into account whether a complete circuit has been formed or not ! Take for example lightning, a high potential is developed in the clouds and current flows as lightning towards earth. So to understand this "unidirectional" flow of current you can consider the current to be as more like a lightning strike, it takes the charge form high potential(hot wire) to low potential(ground).
No There is no path for current to flow through the earth back to the source. so current does not flow. or if you believe there is a path just because the negative terminal is connected to earth and the end point of your circuit is connected to earth then the answer is still no because the resistance is too high. If you dont believe me just put an ameter in the circuit and see if you see any current flowing.
