How much current flows in 10 ohms when connected to 12 volts?

Ohms are the unit of resistance you find in Ohms LAw which says Volts = Amps x Ohms. You can get a voltage drop across a resistance, but would have to know what current is being used and you would have a potentiometer in effect. You are not "converting 12V" to 10V, your are essentially loosing two volts through a resistor.