Hello,
While you MAY have family problems, you also need to remember that there are some rules/practices while @ work.
You can't just walk-away based on YOUR perception/will.
While I do appreciate Abhijit Barua's suggestion, I think there are TWO angles to any & every Resignation:
1] The proof/evidence of resigning [which is what Abhijit Barua is addressing]
2] The factual & professional need for a person to stay on the job--KT or handing-over the responsibilities being just one of them. Having been in the job it's YOUR primary responsibility to hand-over the tasks to whoever is identified to take-over from you.
Suggest talk to your Manager & try to convince him for a reduced Notice Period--which again depends on YOU & the way you convince. If necessary, pl be prepared to share with him the ACTUAL family reasons.
Quite often employees use this [Family problems] as the standard reason to avoid telling the actual facts--for all one knows, they may be joining another job & just wouldn't like to 'waste' [from THEIR perspective] even a single day in the current job.
All the Best.
Rgds,
TS