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When i connected to a original charger for charging my Xperia Z1 overheat it will post a screenshot "the connected power source not sufficient. The battery draining faster then it is charging."
What output does the adapter have?Did you connect to wall socket?
Output :5.0vdc=1500mA
Boot the device in safe mode and charge it like that:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008