I am self teaching myself. I picked up a problem online and need help.

An arc lamp takes 9.6A at 55V. It is operated from a 120V supply. Find the value of the stabiling resistor to be connected in serries.

So I tryed first 120V/9.6A=12.5 ohm. But then I thought a resistor must drop the voltage from 120V to 55V. So then I took voltage devider formula and solved for Rx using 12.5 ohms as R total. I got 5.729 ohms. The answer for the problem is 6.77 ohm.

Thank you for your help.