I am doing an experiment that aims to determine if the rate of electroplating changes with the temperature. I am using a copper rod, a solution of copper(II) ions and a neutral rod to be coated. I also want to keep every other variable the same, which means the voltage across the rods, the concentration of the solution and the current that goes through the circuit. But the times my professor tried to demonstrate electrolysis, either the current or the voltage was always dropping. How do I prevent this from happening? How can I ensure that the voltage and current remain unchanged for the entire duration of a trial?
You can't control both voltage and current electrically: Your power supply will hold one or the other constant, but the properties of the electrolytic cell will then determine the other one.
So you need to hold all of the chemical parts of the experiment constant: Have a large ion bath so that the concentration doesn't change much as the plating takes place. Stir well to keep things mixed. Have large electrodes (i.e. small current density) so that small surface changes don't dominate. Etc.
Try to change the geometry of your electrodes. For example, increase or decrease the distance between the electrodes. This will modify the internal resistance of the solution. So if you have a generator producing a constant voltage, you may reach the desired currant, simply by changing the distance between the electrodes. Of course the electrodes must be hanging at a bar in such a way that their relative position can be adjusted at will by hand.
You could create a constant-current source instead of using an off-the-shelf power supply.
There are also off-the-shelf constant-current supplies, so ask your lab manager if that's a resource. An EE colleague can set this up for you if it's too far outside your domain. Here are a few articles as starting points. Total cost should be < $15.