While you may have family problems, you also need to remember that there are some rules and practices while at work. You can't just walk away based on your perception or will.
While I do appreciate Abhijit Barua's suggestion, I think there are two angles to any and every resignation:
1. The proof or evidence of resigning [which is what Abhijit Barua is addressing].
2. The factual and 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.
I suggest talking to your manager and trying to convince him for a reduced notice period—which again depends on you and the way you convince. If necessary, please 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 and just wouldn't like to 'waste' [from their perspective] even a single day in the current job.
All the best.
Regards, TS