What is the best but cheapset rechargeable battery to use for Galaxy S3?

[AC Question]

I tried the power bank rechargeable battery but it does not take, I thought the first one I bought was bad and when I bought a second one it does the same thing so I know its not a bad battery, my phone is not compatible to it

 

[Rukbat]

"Does not take" doesn't make sense. You plug in the external power source, whether it's a car, a portable charger or a power bank, and the phone should work - unless you've let the phone's battery discharge too far. (You should never let any lithium battery drop below 40% - not even the power bank.)

If the phone's battery is fully drained (a couple of percent or so), you'll have to wait at least a few hours - until the power bank recharges the battery. (The first hour doesn't charge it - it's called "ramp-up", and it's kind of preparation for charging.) I usually recommend waiting 24 hours before trying to turn a phone on if the battery was completely dead. (If it's dead enough, the phone won't even charge it - they you'll have to remove the battery from the phone and use an external "not-as-smart-as-the-phone" charger. Using a power bank will have the same problem - it's just a portable source of 5 Volts, the same, electrically, as a wall charger, as far as the phone is concerned.)

If you want instant use when you drain the battery too far, buy a spare battery or two, keep them fully charged, and keep them in your pocket (in some sort of soft or hard plastic case - a key shorting 2,000mAh lithium battery can get hot enough to start an above the thigh amputation - or even cause the battery to explode, causing a below the waist amputation).. I normally carry a wall charger, one of those USB-on-a-reel cords and a battery in a soft plastic case in my pocket. Have been since around the beginning of the century. (I still have 4 Motorola 7868 batteries and a phone, even though all they're good for now is looking at.)