Question: I have a 11.1 V Li-ion battery pack that I use for a 9-12V device as backup power. When I charge the battery pack, it draws 1-1.25 A of current from the DC charger which has caused more than 1 charger to burn up. How can I limit the current to 0.5 A? I tried using a 47 ohms resistor in series with the battery but it dropped the current to 10 mA. What am I doing wrong?

Answer: 
The problem is that you don't have a lithium battery charger, and you are directly connecting a 12V power supply to your batteries.

Don't do that, as it will damage the power supply and the lithium batteries, and they may explode or burst into flames.

Only charge the lithium batteries with a lithium battery charger.
A Lithium ion battery pack *must* be charged with a circuit specifically designed to do so, and should be discharged with a protection circuit as well. Batteries with multiple cells in series(like yours) should be charged with an appropriate BMS(Battery management system). If you're using Lithium ion for a project, do your research. You might want to check out batteryuniversity.com.