I am not sure but I find "I see" or "I understand" is little bit formal. I am not sure close friends say each other "I see" a lot. I could be wrong, though. It sounds more like a doctor can say it when you talk about your pains.
Here is my scenario
A: Why did you get to class late today?
B: Well, my phone was out of charge (while I was sleeping). So it didn't go off and I missed the train.
C: I see, ok, right or ?
(Could you please rephrase B's the first sentence because I am no sure it is colloquial)