the resistor has a resistance of 3 ohms. If no change in the battery size occurs, what will happen to the current if the resistance increases to 6 ohms?

Quick answer the current will go down.

The formula is

E = I * R. The variation is a direct one. Let us suppose E = 12 volts.

12 = I * 3 ohms Divide both sides by 3

12/3 = I

I = 4 amps

Now do it again for 6 ohms

12 = I * 6 Divide both sides by 6

12/6 = I

I = 2

So the current went down from 4 to 2