If resistance is constant and voltage increases what happens to current?

You have it backwards, the resistance controls the current not the current controls the resistance. I = E/R . Your question should read, "If the voltage is constant and the resistance in the circuit is increased what happens to the current?" Say the voltage is 120 volts and the resistance is 30 ohms, I = 120/30 = 4 amps. Now we double the resistance to 60 ohms, then I = 120/60 = 2 amps. So now you can see if you increase the resistance the current drops.