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I got myself iphone 4 without a battery, I want to buy one, but I’m not sure if I should. I connected it directly to psu (as battery connector was already ripped), and it boots and works fine for like 2 minutes and 20 seconds, and then screen goes dark and it reboots. Is it normal for an iphone without a battery(or rather battery attached only to positive and negative terminals) to do that?

An Iphone will bootloop when connected to power but the battery is removed. To resolve that issue simply purchase and install a new battery.