here 了 is as a modal particle, which means can be used at the end of a statement to show emergence of a new situation or a change in understanding(opinion,ideas or action,etc). 手机关掉了. = My phone is powered off (e.g., I turned it off myself and it is in the off position now). Because the subject of the sencente is I or someone else. And the others I'm agree with Yu Qun.

if battery died and it turned off by itself ，we say '手机关机了'or‘ 手机没电了’ if you turned it off yourself and it is in the off position ,we say '我把手机关掉了'or'我把手机关机了'(you should add 我) 手机关掉了 is more tend to the phone turns off himself 。

eeeeh，Im not good at expressing the English，but I try my best. In china,both of the examples are correct. At first,if you are in bad position, you feel uncomfortable,or you dont want somebody to bother you. you will use this sentence as a excuse.You met a friend who invited you yesterday,but you hadn't gone.when you come across next day,you can say to your friends :"手机关掉了" however,the another possible reason is that the battery is died and it turned off by itself. that's a truth . Friends can't phone you.

I think it depends on how do you say it. If you say "我把手机关掉了", it means the first means you said, but if you say "手机自己关掉了" that means the second means you said. But we often say"手机关机了"

手机关掉了 (the phone is in the off position now, it could be turned off by you or others) 手机关机了(the phone was turned off by itself) 手机没电了(battery died)