Why does my phone keep turning on and off

[AC Question]

My Samsung galaxy alpha turns on and off continuously as soon as I unplug the charger, it doesn't stay on for more than a few seconds.
It means I cannot use my phone unless it is on charge all the time, the power level drops dramatically as soon as I unplug.

 

[belodion]

A faulty battery?

 

[Tim1954]

Or a loose one...