What is the resistance of an electric arc between two graphite electrodes?
Arc lamps have a negative resistance characteristic, so they need some series impedance to stabilize them if you are planning on connecting them to a voltage source. 

You can experiment with something like a 500~1500W (at the supply voltage) heating element such as a small room heater in series with the electrodes. You need a way of  (safely) bringing the rods into contact and then separating them when the carbon gets hot enough to sustain an arc. 

As a WAG I would say the resistance in normal operation is around 5~10 ohms, but has a negative slope so a series resistance of perhaps 10~20 ohms will stabilize the arc and control the current to something reasonable for the size of the rods. 

It cannot be emphasized too strongly that there are many ways to hurt yourself playing around with this- the voltages on the rods are usually high enough to be lethal (perhaps with respect to ground if you're trying to use mains without an isolation transformer- not recommended) and the arc will likely emit strong UV light- that's why they were used in the old plate making machines for offset printing (now replaced by sealed mercury arc lamps).  

Check out the venerable Don Klipstein's page for more info.